The mass formula for self-orthogonal and self-dual codes over a non-unitary commutative ring
In this paper, we establish a mass formula for self-orthogonal codes, quasi self-dual codes, and self-dual codes over commutative non-unital rings $ {{\mathit {I}_p}} = \left < a, b | pa = pb = 0, a^2 = b, ab = 0 \right > $, where $ p $ is an odd prime. We also give a classification of...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
AIMS Press
2023-08-01
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Series: | AIMS Mathematics |
Subjects: | |
Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231242?viewType=HTML |
Summary: | In this paper, we establish a mass formula for self-orthogonal codes, quasi self-dual codes, and self-dual codes over commutative non-unital rings $ {{\mathit {I}_p}} = \left < a, b | pa = pb = 0, a^2 = b, ab = 0 \right > $, where $ p $ is an odd prime. We also give a classification of the three said classes of codes over $ {{\mathit {I}_p}} $ where $ p = 3, 5, $ and $ 7 $, with lengths up to $ 3 $. |
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ISSN: | 2473-6988 |