Affiliation:
1. Department of Mathematics, Jaypee University of Information Technology, Waknaghat 173234, India
Abstract
An MRD code [Formula: see text] is a [Formula: see text]-dimensional [Formula: see text]-linear subspace of the [Formula: see text]-dimensional vector space [Formula: see text] over [Formula: see text] for [Formula: see text]. Linear codes [Formula: see text] (of length [Formula: see text], dimension [Formula: see text]) that are obtained from MRD codes [Formula: see text] satisfying the property [Formula: see text] are defined to be LCD MRD codes. An inherent relationship between the generator G and parity-check matrices H of LCD MRD codes is observed. This in fact identifies LCD MRD codes as trivial ([Formula: see text]) and nontrivial ([Formula: see text]) codes. Further, two classes of LCD MRD codes of length [Formula: see text] are constructed from [Formula: see text] (trivial and nontrivial) LCD MRD codes of length [Formula: see text]. Examples are provided for demonstration of results obtained.
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Characterization of some specific lee distance codes over finite rings;Discrete Mathematics, Algorithms and Applications;2024-06-26
2. Construction of almost self-dual basis from self-dual basis of pn in odd characteristics;5th INTERNATIONAL CONFERENCE ON CURRENT SCENARIO IN PURE AND APPLIED MATHEMATICS (ICCSPAM-2022);2023
3. On Hermitian LCD generalized Gabidulin codes;IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences;2021