Double cyclic codes over $ \aleph =\bigoplus _{i=0}^{n} \zeta ^{i}\mathbb {Z}_{2} $, with $ \zeta ^{n}=0 $

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2025年6月17日

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Zakariae Cheddour

摘要

In this work, we analyze the structure and characteristics of double cyclic codes defined on the ring $ \aleph = \bigoplus _{i=0}^{n} \zeta ^{i}\mathbb {Z}_{2} $ $ℵ = ⨁_{i = 0}^{n} ζ^{i} Z_{2}$ , where $ \zeta ^{n} = 0 $ $ζ^{n} = 0$ . The main objective is to identify the polynomials that generate these types of codes. To do this, we adopt an algebraic approach to develop a constructive method of generation. We also study the ranks and associated minimal covering sets, and determine the conditions that guarantee optimal properties.

Double cyclic codes over \( \aleph =\bigoplus _{i=0}^{n} \zeta ^{i}\mathbb {Z}_{2} \), with \( \zeta ^{n}=0 \)

摘要