The geometry of Hermitian self-orthogonal codes

• URL: http://arxiv.org/abs/2108.08088v1
• Date: Wed, 18 Aug 2021 11:07:13 GMT
• Title: The geometry of Hermitian self-orthogonal codes
• Abstract summary: We prove that truncations of linear codes to codes equivalent to Hermitian self-orthogonal linear codes occur when the columns of a generator matrix of the code do not impose independent conditions on the space of Hermitian forms.
• Score: 0.7614628596146599
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove that if $n >k^2$ then a $k$-dimensional linear code of length $n$ over ${\mathbb F}_{q^2}$ has a truncation which is linearly equivalent to a Hermitian self-orthogonal linear code. In the contrary case we prove that truncations of linear codes to codes equivalent to Hermitian self-orthogonal linear codes occur when the columns of a generator matrix of the code do not impose independent conditions on the space of Hermitian forms. In the case that there are more than $n$ common zeros to the set of Hermitian forms which are zero on the columns of a generator matrix of the code, the additional zeros give the extension of the code to a code that has a truncation which is equivalent to a Hermitian self-orthogonal code.

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