Additive one-rank hull codes over finite fields

Fuente: arXiv
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Autori principali: Agrawal, Astha, Sharma, R. K.
Natura: Preprint
Pubblicazione: 2023
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author Agrawal, Astha
Sharma, R. K.
author_facet Agrawal, Astha
Sharma, R. K.
contents This article explores additive codes with one-rank hull, offering key insights and constructions. The article introduces a novel approach to finding one-rank hull codes over finite fields by establishing a connection between self-orthogonal elements and solutions of quadratic forms. It also provides a precise count of self-orthogonal elements for any duality over the finite field $\mathbb{F}_q$, particularly odd primes. Additionally, construction methods for small rank hull codes are introduced. The highest possible minimum distance among additive one-rank hull codes is denoted by $d_1[n,k]_{p^e,M}$. The value of $d_1[n,k]_{p^e,M}$ for $k=1,2$ and $n\geq 2$ with respect to any duality $M$ over any finite field $\mathbb{F}_{p^e}$ is determined. Furthermore, the new quaternary one-rank hull codes are identified over non-symmetric dualities with better parameters than symmetric ones.
format Preprint
id arxiv_https___arxiv_org_abs_2310_08074
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Additive one-rank hull codes over finite fields
Agrawal, Astha
Sharma, R. K.
Information Theory
Primary 94B60, Secondary 94B99
This article explores additive codes with one-rank hull, offering key insights and constructions. The article introduces a novel approach to finding one-rank hull codes over finite fields by establishing a connection between self-orthogonal elements and solutions of quadratic forms. It also provides a precise count of self-orthogonal elements for any duality over the finite field $\mathbb{F}_q$, particularly odd primes. Additionally, construction methods for small rank hull codes are introduced. The highest possible minimum distance among additive one-rank hull codes is denoted by $d_1[n,k]_{p^e,M}$. The value of $d_1[n,k]_{p^e,M}$ for $k=1,2$ and $n\geq 2$ with respect to any duality $M$ over any finite field $\mathbb{F}_{p^e}$ is determined. Furthermore, the new quaternary one-rank hull codes are identified over non-symmetric dualities with better parameters than symmetric ones.
title Additive one-rank hull codes over finite fields
topic Information Theory
Primary 94B60, Secondary 94B99
url https://arxiv.org/abs/2310.08074