Bibliographische Detailangaben
| Titel: |
Binary subfield codes of codes over a certain chain ring. |
| Autoren: |
Bhagat, Anuj Kumar, Sagar, Vidya, Sarma, Ritumoni |
| Quelle: |
Advances in Mathematics of Communications; Aug2025, Vol. 19 Issue 4, p1-16, 16p |
| Schlagwörter: |
LINEAR codes, BINARY codes |
| Abstract: |
In this article, we consider linear codes over the chain ring $ \frac{\mathbb{F}_{2}[x]}{\langle x^s\rangle} $ with $ s\geq 2 $ that are obtained using a construction referred to as the $ \mathcal{C}_D $-construction, where $ D $ is a set generated with the help of certain simplicial complexes. The main result is the utilization of the trace map $ \tau:\mathbb{F}_{2}[x]/\langle x^s\rangle\longrightarrow \mathbb{F}_2 $ given by $ a_0+a_1u+a_2u^2+\cdots+a_{s-1}u^{s-1}\mapsto a_0+a_1+\cdots+a_{s-1} $ to study binary subfield codes of $ \mathcal{C}_D $-codes. These binary subfield codes are $ l $-weight codes where $ l = 1, 2 $, or $ 4 $, and most of them are distance-optimal codes. Moreover, these binary codes are self-orthogonal and minimal under certain conditions. We present many new distance-optimal binary linear codes. [ABSTRACT FROM AUTHOR] |
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| Datenbank: |
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