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.

Constant weight codes based on ideals of commutative rings

We present a construction of constant weight codes based on the prime ideals of a Noetherian commutative ring. The coding scheme is based on the uniqueness of the primary decomposition of ideals in Noetherian rings. The source alphabet consists of a set of radical ideals constructed from a chosen subset of the prime spectrum of the ring. The distance function between two radical ideals is taken to be the Hamming metric based on the symmetric distance between sets. As an application we construct codes for random networks employing SAF routing.

New Bounds for the Maximum Size of Ternary Constant Weight Codes

This work was partially supported by the Bulgarian National Science Fund under Grant I–618/96.

Second-order rate region of constant-composition codes for the multiple-access channel

This paper presents an achievable second-order rate region for the discrete memoryless multiple-access channel. The result is obtained using a random-coding ensemble in which each user's codebook contains codewords of a fixed composition. It is shown that this ensemble performs at least as well as i.i.d. random coding in terms of second-order asymptotics, and an example is given where a strict improvement is observed. © 2013 IEEE.

Noise Reduction Using Low Weight and Constant Weight Coding Techniques

Signalling off-chip requires significant current. As a result, a chip's power-supply current changes drastically during certain output-bus transitions. These current fluctuations cause a voltage drop between the chip and circuit board due to the parasitic inductance of the power-supply package leads. Digital designers often go to great lengths to reduce this "transmitted" noise. Cray, for instance, carefully balances output signals using a technique called differential signalling to guarantee a chip has constant output current. Transmitted-noise reduction costs Cray a factor of two in output pins and wires. Coding achieves similar results at smaller costs.

Efficient information reconciliation for Continuous-Variable QKD using Non-Binary Low-Density Parity-Check Codes

We present here an information reconciliation method and demonstrate for the first time that it can achieve efficiencies close to 0.98. This method is based on the belief propagation decoding of non-binary LDPC codes over finite (Galois) fields. In particular, for convenience and faster decoding we only consider power-of-two Galois fields.

Improvements on the Juxtaposing Theorem

A new class of binary constant weight codes is presented. We establish new lower bound and exact values on A(n1 +n2; 2(a1 +a2); n2) ≥ min {M1;M2}+1, if A(n1; 2a1; a1 +b1) = M1 and A(n2; 2b2; a2 +b2) = M2, in particular, A(30; 16; 15) = 16 and A(33; 18; 15) = 11.

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.

Different approaches of applying single-objective binary genetic algorithm on the wind farm design

This paper discusses three different ways of applying the single-objective binary genetic algorithm into designing the wind farm. The introduction of different applications is through altering the binary encoding methods in GA codes. The first encoding method is the traditional one with fixed wind turbine positions. The second involves varying the initial positions from results of the first method, and it is achieved by using binary digits to represent the coordination of wind turbine on X or Y axis. The third is the mixing of the first encoding method with another one, which is by adding four more binary digits to represent one of the unavailable plots. The goal of this paper is to demonstrate how the single-objective binary algorithm can be applied and how the wind turbines are distributed under various conditions with best fitness. The main emphasis of discussion is focused on the scenario of wind direction varying from 0° to 45°. Results show that choosing the appropriate position of wind turbines is more significant than choosing the wind turbine numbers, considering that the former has a bigger influence on the whole farm fitness than the latter. And the farm has best performance of fitness values, farm efficiency, and total power with the direction between 20°to 30°.

Spatial neighborhood matrix computation: Inverse distance weighted versus binary contiguity

Paper presented at Geo-Spatial Crossroad GI_Forum, Salzburg, Austria.

Construction of I-Deletion-Correcting Ternary Codes

Finding large deletion correcting codes is an important issue in coding theory. Many researchers have studied this topic over the years. Varshamov and Tenegolts constructed the Varshamov-Tenengolts codes (VT codes) and Levenshtein showed the Varshamov-Tenengolts codes are perfect binary one-deletion correcting codes in 1992. Tenegolts constructed T codes to handle the non-binary cases. However the T codes are neither optimal nor perfect, which means some progress can be established. Latterly, Bours showed that perfect deletion-correcting codes have a close relationship with design theory. By this approach, Wang and Yin constructed perfect 5-deletion correcting codes of length 7 for large alphabet size. For our research, we focus on how to extend or combinatorially construct large codes with longer length, few deletions and small but non-binary alphabet especially ternary. After a brief study, we discovered some properties of T codes and produced some large codes by 3 different ways of extending some existing good codes.

Weight loss and surface roughness of hard chairside reline resins after toothbrushing: Influence of postpolymerization treatments

Purpose: To evaluate the effect of 2 postpolymerization treatments on toothbrushing wear (weight loss) and surface roughness of 3 autopolymerized reline resins-Duraliner II (D) (Reliance Dental), Kooliner (K) (Coe Laboratories), and Tokuso Rebase Fast (T) (Tokuyama Dental)-and 1 heat-polymerized resin, Lucitone 550 (L) (Dentsply International). Materials and Methods: Specimens (40 x 10 x 2mm) of each material (n = 24) were prepared and divided into 3 groups: control (no postpolymerization treatment); water bath (immersion in water at 55°C); and microwave (microwave irradiation). Specimens were dried until constant weight was achieved and the surface roughness (Ra) was measured. Tests were performed in a toothbrush machine using 20,000 strokes of brushing at a weight of 200 g, with the specimens immersed in 1:1 dentifrice/water slurry. Specimens were reconditioned to constant weight and the weight loss (mg) and surface roughness were evaluated. Data were analyzed by 2-way analysis of variance and followed by Tukey test (α = .05). Results: In the control group, the weight loss of materials D and T was lower (P < .05) than that of L. No differences among materials were found after postpolymerization treatments (P > .05). The weight loss of material T (control = 0.5 mg) was significantly increased (P < .05) after postpolymerization treatments (water bath = 1.9 mg; microwave = 1.8 mg). For materials K and T, the toothbrushed surface roughness was higher (P < .05) after microwave and waterbath postpolymerization treatments. Material L showed increased surface roughness after microwave postpolymerization treatment. Conclusion: The toothbrushing wear resistance of L was not superior to the reline resins. The postpolymerization treatments did not improve the toothbrushing wear resistance of the materials and produced an increased surface roughness for materials L, K, and T.

A formalized optimum code search for q-ary trellis codes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Interleavers and BCH codes for coherent DQPSK systems with laser phase noise

The relatively high phase noise of coherent optical systems poses unique challenges for forward error correction (FEC). In this letter, we propose a novel semianalytical method for selecting combinations of interleaver lengths and binary Bose-Chaudhuri-Hocquenghem (BCH) codes that meet a target post-FEC bit error rate (BER). Our method requires only short pre-FEC simulations, based on which we design interleavers and codes analytically. It is applicable to pre-FEC BER ∼10-3, and any post-FEC BER. In addition, we show that there is a tradeoff between code overhead and interleaver delay. Finally, for a target of 10-5, numerical simulations show that interleaver-code combinations selected using our method have post-FEC BER around 2× target. The target BER is achieved with 0.1 dB extra signal-to-noise ratio.

Dimensioning BCH codes for coherent DQPSK systems with laser phase noise and cycle slips

Forward error correction (FEC) plays a vital role in coherent optical systems employing multi-level modulation. However, much of coding theory assumes that additive white Gaussian noise (AWGN) is dominant, whereas coherent optical systems have significant phase noise (PN) in addition to AWGN. This changes the error statistics and impacts FEC performance. In this paper, we propose a novel semianalytical method for dimensioning binary Bose-Chaudhuri-Hocquenghem (BCH) codes for systems with PN. Our method involves extracting statistics from pre-FEC bit error rate (BER) simulations. We use these statistics to parameterize a bivariate binomial model that describes the distribution of bit errors. In this way, we relate pre-FEC statistics to post-FEC BER and BCH codes. Our method is applicable to pre-FEC BER around 10-3 and any post-FEC BER. Using numerical simulations, we evaluate the accuracy of our approach for a target post-FEC BER of 10-5. Codes dimensioned with our bivariate binomial model meet the target within 0.2-dB signal-to-noise ratio.