Decoding beyond the designed distance for certain algebraic codes

Fast decoding of algebraic-geometric codes up to the designed minimum distance

We present a decoding algorithm for algebraicgeometric codes from regular plane curves, in particular the Hermitian curve, which corrects all error patternes of weight less than d*/2 with low complexity. The algorithm is based on the majority scheme of Feng and Rao and uses a modified version of Sakata’s generalization of the Berlekamp-Massey algorithm.

Decoding Reed-Muller Codes beyond Half the Minimum Distance

Decoding method for generalized algebraic geometry codes

We propose a decoding method for the generalized algebraic geometry codes proposed by Xing et al. To show its practical usefulness, we give an example of generalized algebraic geometry codes of length 567 over F8 whose numbers of correctable errors by the proposed method are larger than the shortened codes of the primitive BCH codes of length 4095 in the most range of dimension.

An algebraic approach for decoding spread codes

We present a family of constant–dimension codes for random linear network coding called spread codes. This is a family of optimal codes with maximum minimum distance. A spread code is constructed starting from the algebra defined by the companion matrix of an irreducible polynomial. We give a minimum distance decoding algorithm that is particularly efficient when the dimension of the codewords ...

Algebraic decoding for doubly cyclic convolutional codes

An iterative decoding algorithm for convolutional codes is presented. It successively processes N consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be corrected. The algorithm can be efficiently used on a particular class of convolutional codes, known as doubly cyclic convolutional codes. Due to their highly a...