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arXiv · 1809.07090

Characteristic vector and weight distribution of a linear code

Iliya Bouyukliev·Stefka Bouyuklieva·Tatsuya Maruta·Paskal Piperkov
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Abstract

We develop an algorithm for computing the weight distribution of a linear $[n,k]$ code over a finite field $\mathbb{F}_q$. We represent the codes by their characteristic vector with respect to a given generator matrix and a special type of a generator matrix of the k-dimensional simplex code. This characteristic vector is the input data of our algorithms. The complexity of the presented algorithms is O(kq^k).

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Iliya Bouyukliev, Stefka Bouyuklieva, Tatsuya Maruta, Paskal Piperkov. 2018-09-19. Characteristic vector and weight distribution of a linear code. https://doi.org/10.1007/s12095-020-00458-8

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