2017/07/17 by Sharma, Anuradha, Chauhan, Varsha, Singh, Harshdeep · 1 citation
#94B15 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1707.05039
Let \mathbbFq denote the finite field of order q, let m1,m2,⋯,mℓ be positive integers satisfying gcd(mi,q)=1 for 1 ≤ i ≤ ℓ, and let n=m1+m2+⋯+mℓ. Let Λ=(λ1,λ2,⋯,λℓ) be fixed, where λ1,λ2,⋯,λℓ are non-zero elements of \mathbbFq. In this paper, we study the algebraic structure of Λ-multi-twisted codes of length n over \mathbbFq and their dual codes with respect to the standard inner product on \mathbbFqn. We provide necessary and sufficient conditions for the existence of a self-dual Λ-multi-twisted code of length n over \mathbbFq, and obtain enumeration formulae for all self-dual and self-orthogonal Λ-multi-twisted codes of length n over \mathbbFq. We also derive some sufficient conditions under which a Λ-multi-twisted code is LCD. We determine the parity-check polynomial of all Λ-multi-twisted codes of length n over \mathbbFq and obtain a BCH type bound on their minimum Hamming distances. We also determine generating sets of dual codes of some Λ-multi-twisted codes of length n over \mathbbFq from the generating sets of the codes. Besides this, we provide a trace description for all Λ-multi-twisted codes of length n over \mathbbFq 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.