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arXiv · 1502.02927

On the shape of the general error locator polynomial for cyclic codes

Fabrizio Caruso·Emmanuela Orsini·Massimiliano Sala·Claudia Tinnirello
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Abstract

A general result on the explicit form of the general error locator polynomial for all cyclic codes is given, along with several results for infinite classes of cyclic codes with $t=2$ and $t=3$. From these, a theoretically justification of the sparsity of the general error locator polynomial is obtained for all cyclic codes with $t\leq 3$ and $n<63$, except for three cases where the sparsity is proved by a computer check. Moreover, we discuss some consequences of our results to the understanding of the complexity of bounded-distance decoding of cyclic codes.

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Fabrizio Caruso, Emmanuela Orsini, Massimiliano Sala, Claudia Tinnirello. 2015-12-24. On the shape of the general error locator polynomial for cyclic codes. https://arxiv.org/abs/1502.02927

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