Decoding Algorithms For Linear Codes Research Articles

Decoding Linear Codes over Chain Rings Given by Parity Check Matrices

We design a decoding algorithm for linear codes over finite chain rings given by their parity check matrices. It is assumed that decoding algorithms over the residue field are known at each degree of the adic decomposition.

Linear Codes over $\mathbb{F}_{q}[u]/(u^s)$ with Respect to the Rosenbloom–Tsfasman Metric

We investigate the structure of codes over $\mathbb{F}_q[u]/(u^s)$ rings with respect to the Rosenbloom-Tsfasman (RT) metric. We define a standard form generator matrix and show how we can determine the minimum distance of a code by taking advantage of its standard form. We define MDR (maximum distance rank) codes with respect to this metric and give the weights of the codewords of an MDR code. We explore the structure of cyclic codes over $\mathbb{F}_q[u]/(u^s)$ and show that all cyclic codes over $\mathbb{F}_q[u]/(u^s)$ rings are MDR. We propose a decoding algorithm for linear codes over these rings with respect to the RT metric.

Hard- and soft-decision decoding beyond the half minimum distance---An algorithm for linear codes (Corresp.)

A decoding algorithm for linear codes that uses the minimum weight words of the dual code as parity checks is defined. This algorithm is able to correct beyond the half minimum distance and has the capability of including soft-decision decoding. Results on applying this algorithm to quadratic residue (QR) codes, BCH codes, and the Golay codes (with and without soft-decision decoding) are presented.

Efficient decoding algorithms for linear codes on soft-quantized channels (Ph.D. Thesis abstr.)

Efficient decoding algorithms for linear codes on soft-quantized channels (Ph.D. Thesis abstr.)