Minimum Distance of New Generalizations of the Punctured Binary Reed-Muller Codes
Abstract
Motivated by applications in combinatorial design theory and constructing LCD codes, C. Ding et al \cite{DLX} introduced cyclic codes $\mho(q,m,h)$ and $\bar\mho(q,m,h)$ over $\mathbb{F}_q$ as new generalization and version of the punctured binary Reed-Muller codes. In this paper, we show several new results on minimum distance of $\mho(q,m,h)$ and $\bar\mho(q,m,h)$ which are generalization or improvement of previous results given in \cite{DLX}.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2018
- DOI:
- 10.48550/arXiv.1805.10562
- arXiv:
- arXiv:1805.10562
- Bibcode:
- 2018arXiv180510562H
- Keywords:
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- Computer Science - Information Theory
- E-Print:
- 11 pages, 2 tables