Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895666 | Finite Fields and Their Applications | 2018 | 28 Pages |
Abstract
Let Fq denote the finite field of order q, let m1,m2,â¯,mâ be positive integers satisfying gcdâ¡(mi,q)=1 for 1â¤iâ¤â, and let n=m1+m2+â¯+mâ. Let Î=(λ1,λ2,â¯,λâ) be fixed, where λ1,λ2,â¯,λâ are non-zero elements of Fq. In this paper, we study the algebraic structure of Î-multi-twisted codes of length n over Fq and their dual codes with respect to the standard inner product on Fqn. We provide necessary and sufficient conditions for the existence of a self-dual Î-multi-twisted code of length n over Fq, and obtain enumeration formulae for all self-dual and self-orthogonal Î-multi-twisted codes of length n over Fq. We also derive some sufficient conditions under which a Î-multi-twisted code is linear with complementary dual (LCD). We determine the parity-check polynomial of all Î-multi-twisted codes of length n over Fq and obtain a BCH type bound on their minimum Hamming distances. We also determine generating sets of dual codes of some Î-multi-twisted codes of length n over Fq from the generating sets of the codes. Besides this, we provide a trace description for all Î-multi-twisted codes of length n over Fq by viewing these codes as direct sums of certain concatenated codes, which leads to a method to construct these codes. We also obtain a lower bound on their minimum Hamming distances using their multilevel concatenated structure.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Anuradha Sharma, Varsha Chauhan, Harshdeep Singh,