Weight hierarchies of a family of linear codes associated with degenerate quadratic forms

Fei Li; Xiumei Li

doi:10.1016/j.disc.2021.112718

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arXiv · 1804.06866

Weight hierarchies of a family of linear codes associated with degenerate quadratic forms

Fei Li·Xiumei Li

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Abstract

We restrict a degenerate quadratic form $f$ over a finite field of odd characteristic to subspaces. Thus, a quotient space related to $f$ is introduced. Then we get a non-degenerate quadratic form induced by $f$ over the quotient space. Some related results on the subspaces and quotient space are obtained. Based on this, we solve the weight hierarchies of a family of linear codes related to $f.$

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Fei Li, Xiumei Li. 2018-04-18. Weight hierarchies of a family of linear codes associated with degenerate quadratic forms. https://doi.org/10.1016/j.disc.2021.112718

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