Computing coset leaders of binary codes

Details Computing coset leaders of binary codes Computing coset leaders of binary codes

2010-01-28

arxiv.org/abs/1001.5074v1

Computer Science

Information Theory

Submitted to Designs, Codes and Cryptography

Scientific paper

We present an algorithm for computing the set of all coset leaders of a binary code $\mathcal C \subset \mathbb{F}_2^n$. The method is adapted from some of the techniques related to the computation of Gr\"obner representations associated with codes. The algorithm provides a Gr\"obner representation of the binary code and the set of coset leaders $\mathrm{CL}(\mathcal C)$. Its efficiency stands of the fact that its complexity is linear on the number of elements of $\mathrm{CL}(\mathcal C)$, which is smaller than exhaustive search in $\mathbb{F}_2^n$.

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