On Extremal Binary Doubly-Even Self-Dual Codes of Length 88*

In this paper we present 35 new extremal binary self-dual doubly-even codes of length 88. Their inequivalence is established by invariants. Moreover, a construction of a binary self-dual [88, 44, 16] code, having an automorphism of order 21, is given.

The Nonexistence of [132, 6, 86]3 Codes and [135, 6, 88]3 Codes

We prove the nonexistence of [g3(6, d), 6, d]3 codes for d = 86, 87, 88, where g3(k, d) = ∑⌈d/3i⌉ and i=0 ... k−1. This determines n3(6, d) for d = 86, 87, 88, where nq(k, d) is the minimum length n for which an [n, k, d]q code exists.

Note on an Improvement of the Griesmer Bound for q-ary Linear Codes

Let nq(k, d) denote the smallest value of n for which an [n, k, d]q code exists for given integers k and d with k ≥ 3, 1 ≤ d ≤ q^(k−1) and a prime or a prime power q. The purpose of this note is to show that there exists a series of the functions h3,q, h4,q, ..., hk,q such that nq(k, d) can be expressed.

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.