We show that an optimal source code with cost function for code symbols can be regarded as a random number generator generating a random sequence (not necessarily a sequence of fair coin bits) as the target distribution in the sense that the normalized conditional divergence between the distribution of the generated codeword distribution and the target distribution vanishes as the block length ...

A new Gray map which is both an isometry and a weight preserving map from R = F2 + vF2 + v 2F2 to F 3 2 is defined. A construction for quantum error correcting codes from cyclic codes over finite ring R = F2 + vF2 + v 2F2, v 3 = v is given.The parameters of quantum codes which are obtained from cyclic codes over R are determined.

This work applies earlier results on Quasi-Cyclic (QC) LDPC codes to the codes specified in six separate IEEE 802 standards, specifying wireless communications from 54 MHz to 60 GHz. First, we examine the weight matrices specified to upper bound the codes’ minimum distance independent of block length. Next, we search for the minimum distance achieved for the parity check matrices selected at ea...

In this paper, we construct an infinite family of three-weight binary codes from linear codes over the ring R = F2+ vF2+ v 2 F2, where v 3 = 1. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distributions are computed by employing character sums. The three-weight binary linear codes which we construct are shown to be optimal when m i...

The purpose of this paper is to discuss the importance of algebraic coding theory and to investigate the special case in which BIB designs and codes are constructed from planar near-rings. Application of planar near-rings to binary codes were first explored by Modisett [12] and by Fuchs, Hofer and Pilz [14]. Key word: planar near-ring, incidence structure, tactical configuration, BIBD, binary c...

The performance of a Turbo code with short block length depends critically on the interleaver design. There are two major criteria in the design of an interleaver: the distance spectrum of the code and the correlation between the information input data and the soft output of each decoder corresponding to its parity bits. This paper describes a new interleaver design for Turbo codes with short b...

We construct a large number of record-breaking binary, ternary and quaternary codes. Our methods involve the study of BCH-codes over larger fields, concatenation, construction X and variants of the Griesmer construction (residual codes). 1 Review of the theory Let IFq be the ground field, F = IFq2 . Denote the interval {i, i + 1, . . . , j} ⊂ ZZ/(q−1)ZZ by [i, j]. Let A = [i, j] ⊂ ZZ/(q−1)ZZ. I...

Systematic polar codes are shown to outperform non-systematic polar codes in terms of the bit-error-rate (BER) performance. However theoretically the mechanism behind the better performance of systematic polar codes is not yet clear. In this paper, we set the theoretical framework to analyze the performance of systematic polar codes. The exact evaluation of the BER of systematic polar codes con...

We study properties of binary codes with parameters close to the parameters of 1-perfect codes. An arbitrary binary (n = 2 − 3, 2n−m−1, 4) code C, i.e., a code with parameters of a triply-shortened extended Hamming code, is a cell of an equitable partition of the n-cube into six cells. An arbitrary binary (n = 2−4, 2, 3) codeD, i.e., a code with parameters of a triply-shortened Hamming code, is...

It has been well-known that the class of quasi-cyclic (QC) codes contain many good codes. In this paper, a method to conduct a computer search for binary 2-generator QC codes is presented, and a large number of good 2-generator QC codes have been obtained. 5 new binary QC codes that improve the lower bounds on minimum distance are presented. Furthermore, with new 2-generator QC codes and Constr...