Minimal Codewords in Linear Codes

2000 Mathematics Subject Classification: 94B05, 94B15.

Dimensioning RS codes for mitigation of phase noise induced cycle slips in DQPSK systems

We present a semi-analytical method for dimensioning Reed-Solomon codes for coherent DQPSK systems with laser phase noise and cycle slips. We evaluate the accuracy of our method for a 28 Gbaud system using numerical simulations.

On Binary Self-Dual Codes of Length 62 with an Automorphism of Order 7

Николай Янков - Класифицирани са с точност до еквивалетност всички оптимални двоични самодуални [62, 31, 12] кодове, които притежават автоморфизъм от ред 7 с 8 независими цикъла при разлагане на независими цикли. Използвайки метода за конструиране на самодуални кодове, притежаващи автоморфизъм от нечетен прост ред е доказано, че съществуват точно 8 нееквивалентни такива кода. Три от получените кодове имат тегловна функция, каквато досега не бе известно да съществува.

Construction of Optimal Linear Codes by Geometric Puncturing

Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4.

Extending the GUIDE@HAND Tourist Guide Application with QR Codes for Museum Learning

The following paper attempts to encompass the opportunities for applying QR codes for museums and exhibits through the example of the Hungarian Museum of Environmental Protection and Water Management (Esztergom, Hungary). Besides providing interactivity in the museum for the mobile phone generation through the utilization of a device and a method that they are familiar with, it is important to explain how and why it is worthwhile to “adorn” the exhibits with these codes. In this paper we also touch upon the technical issues of how an existing mobile phone application can be incorporated into and used for the presentation of the museum.

Mobile Exploring of the Bulgarian Iconography through QR Codes in the GUIDE@HAND Tourist Guide Application

The following paper presents an application of QR code marking of digital iconographical collections for their outdoor mobile access and exploring through the GUIDE@HAND audio tourist guide.

Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths

Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant weight codes. Therefore the classification of (v, 3, 1) OOCs holds for them too. Some of the classified (v, 3, 1) OOCs are perfect and they are equivalent to cyclic Steiner triple systems of order v and (v, 3, 1) cyclic difference families.

Concurrent codes:a holographic-type encoding robust against noise and loss

Concurrent coding is an encoding scheme with 'holographic' type properties that are shown here to be robust against a significant amount of noise and signal loss. This single encoding scheme is able to correct for random errors and burst errors simultaneously, but does not rely on cyclic codes. A simple and practical scheme has been tested that displays perfect decoding when the signal to noise ratio is of order -18dB. The same scheme also displays perfect reconstruction when a contiguous block of 40% of the transmission is missing. In addition this scheme is 50% more efficient in terms of transmitted power requirements than equivalent cyclic codes. A simple model is presented that describes the process of decoding and can determine the computational load that would be expected, as well as describing the critical levels of noise and missing data at which false messages begin to be generated.

Weakly-constrained codes for suppression of patterning effects in digital communications

We propose weakly-constrained stream and block codes with tunable pattern-dependent statistics and demonstrate that the block code capacity at large block sizes is close to the the prediction obtained from a simple Markov model published earlier. We demonstrate the feasibility of the code by presenting original encoding and decoding algorithms with a complexity log-linear in the block size and with modest table memory requirements. We also show that when such codes are used for mitigation of patterning effects in optical fibre communications, a gain of about 0.5dB is possible under realistic conditions, at the expense of small redundancy 10%). © 2006 IEEE.

A case study of the assignment of withdrawal codes for reporting dropout in two disciplinary alternative schools

Dropout rates are major issues facing any nation's continued economic and social progress. The seriousness of this issue in the United States is evidenced by the recent legislation of the 2001 No Child Left Behind Act. The purpose of this study was to use the richness of qualitative methodology to analyze inaccuracies in the assignment of withdrawal codes by school administrators in two different disciplinary alternative schools. The primary codes examined were Code 05, any students over the age of 16 who leaves school voluntarily with no intention of returning; Code 15, any PK–12 student who is withdrawn from school due to nonattendance; Code 22, whereabouts unknown; Code 23, no other code can be used to identify the student's reason for leaving school, and Code 26, entering an adult program. ^ The cross-case method was used for this study. The participants were comprised of 19 school personnel and 25 students from two disciplinary alternative schools, designated X and Y, in the Miami-Dade County Public School system, Miami, FL. Data collection procedures included semi-structured interview, observations, field notes, and district documents. With a matrix, these data were analyzed to compare patterns and themes that emerged within both schools. ^ Results indicated that withdrawal codes were assigned inaccurately for two distinct reasons. At School Y, withdrawal codes were inaccurately assigned intentionally to keep the students from returning to a regular school without notification. At School X, withdrawal codes were inaccurately assigned due to lack of ability to properly track students and ascertain the real circumstances for their departure from school. The end result in both cases was that the school systems were not accurately identifying the whereabouts of students. It was recommended that further investigation be conducted to compare the accuracy of reporting dropouts among traditional/regular high schools and disciplinary alternative schools. ^

A Case Study of the Assignment of Withdrawal Codes for Reporting Dropouts in Two Disciplinary Alternative Schools

This study examined assignment of withdrawal codes by school administrators in two disciplinary alternative schools. Findings revealed: (a) codes were inaccurately assigned intentionally to keep students from returning to a regular school without notification, and (b) administrators improperly tracked students and failed to ascertain students’ reasons for dropping out.

(Table 1) Individual codes, haplotype codes, GenBank accession numbers for DNA sequences and sample locality of the analysed Betamorpha fusiformis specimens from the ANDEEP III expedition

Based on our current knowledge about population genetics, phylogeography and speciation, we begin to understand that the deep sea harbours more species than suggested in the past. Deep-sea soft-sediment environment in particular hosts a diverse and highly endemic invertebrate fauna. Very little is known about evolutionary processes that generate this remarkable species richness, the genetic variability and spatial distribution of deep-sea animals. In this study, phylogeographic patterns and the genetic variability among eight populations of the abundant and widespread deep-sea isopod morphospecies Betamorpha fusiformis [Barnard, K.H., 1920. Contributions to the crustacean fauna of South Africa. 6. Further additions to the list of marine isopods. Annals of the South African Museum 17, 319-438] were examined. A fragment of the mitochondrial 16S rRNA gene of 50 specimens and the complete nuclear 18S rRNA gene of 7 specimens were sequenced. The molecular data reveal high levels of genetic variability of both genes between populations, giving evidence for distinct monophyletic groups of haplotypes with average p-distances ranging from 0.0470 to 0.1440 (d-distances: 0.0592-0.2850) of the 16S rDNA, and 18S rDNA p-distances ranging between 0.0032 and 0.0174 (d-distances: 0.0033-0.0195). Intermediate values are absent. Our results show that widely distributed benthic deep-sea organisms of a homogeneous phenotype can be differentiated into genetically highly divergent populations. Sympatry of some genotypes indicates the existence of cryptic speciation. Flocks of closely related but genetically distinct species probably exist in other widespread benthic deep-sea asellotes and other Peracarida. Based on existing data we hypothesize that many widespread morphospecies are complexes of cryptic biological species (patchwork hypothesis).

R-codes, and coral abundance, water temperature and transect characteristics of nearshore reefs in Belize

Coral reefs are increasingly threatened by global and local anthropogenic stressors, such as rising seawater temperature and nutrient enrichment. These two stressors vary widely across the reef face and parsing out their influence on coral communities at reef system scales has been particularly challenging. Here, we investigate the influence of temperature and nutrients on coral community traits and life history strategies on lagoonal reefs across the Belize Mesoamerican Barrier Reef System (MBRS). A novel metric was developed using ultra-high-resolution sea surface temperatures (SST) to classify reefs as enduring low (lowTP), moderate (modTP), or extreme (extTP) temperature parameters over 10 years (2003 to 2012). Chlorophyll-a (chl a) records obtained for the same interval were employed as a proxy for bulk nutrients and these records were complemented with in situ measurements to "sea truth" nutrient content across the three reef types. Chl a concentrations were highest at extTP sites, medial at modTP sites and lowest at lowTP sites. Coral species richness, abundance, diversity, density, and percent cover were lower at extTP sites compared to lowTP and modTP sites, but these reef community traits did not differ between lowTP and modTP sites. Coral life history strategy analyses showed that extTP sites were dominated by hardy stress-tolerant and fast-growing weedy coral species, while lowTP and modTP sites consisted of competitive, generalist, weedy, and stress-tolerant coral species. These results suggest that differences in coral community traits and life history strategies between extTP and lowTP/modTP sites were driven primarily by temperature differences with differences in nutrients across site types playing a lesser role. Dominance of weedy and stress-tolerant genera at extTP sites suggests that corals utilizing these two life history strategies may be better suited to cope with warmer oceans and thus may warrant further protective status during this climate change interval. Data associated with this project are archived here, including: -SST data -Satellite Chl a data -Nutrient measurements -Raw coral community survey data For questions contact Justin Baumann (j.baumann3 gmail.com)

Error tolerance of topological codes with independent bit-flip and measurement errors

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).