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Let $mathbb{F}_{q}$ denote the finite field of order $q,$ let $m_1,m_2,cdots,m_{ell}$ be positive integers satisfying $gcd(m_i,q)=1$ for $1 leq i leq ell,$ and let $n=m_1+m_2+cdots+m_{ell}.$ Let $Lambda=(lambda_1,lambda_2,cdots,lambda_{ell})$ be fixed, where $lambda_1,lambda_2,cdots,lambda_{ell}$ are non-zero elements of $mathbb{F}_{q}.$ In this paper, we study the algebraic structure of $Lambda$-multi-twisted codes of length $n$ over $mathbb{F}_{q}$ and their dual codes with respect to the standard inner product on $mathbb{F}_{q}^n.$ We provide necessary and sufficient conditions for the existence of a self-dual $Lambda$-multi-twisted code of length $n$ over $mathbb{F}_{q},$ and obtain enumeration formulae for all self-dual and self-orthogonal $Lambda$-multi-twisted codes of length $n$ over $mathbb{F}_{q}.$ We also derive some sufficient conditions under which a $Lambda$-multi-twisted code is LCD. We determine the parity-check polynomial of all $Lambda$-multi-twisted codes of length $n$ over $mathbb{F}_{q}$ and obtain a BCH type bound on their minimum Hamming distances. We also determine generating sets of dual codes of some $Lambda$-multi-twisted codes of length $n$ over $mathbb{F}_{q}$ from the generating sets of the codes. Besides this, we provide a trace description for all $Lambda$-multi-twisted codes of length $n$ over $mathbb{F}_{q}$ 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.
In this paper, we produce new classes of MDS self-dual codes via (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. Among our constructions, there are many MDS self-dual codes with new parameters which have never been
In this paper, we present three new classes of $q$-ary quantum MDS codes utilizing generalized Reed-Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some $q$-ary quantum MDS codes can be bi
Self-dual codes over $Z_2timesZ_4$ are subgroups of $Z_2^alpha timesZ_4^beta$ that are equal to their orthogonal under an inner-product that relates to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible
This paper considers the construction of isodual quasi-cyclic codes. First we prove that two quasi-cyclic codes are permutation equivalent if and only if their constituent codes are equivalent. This gives conditions on the existence of isodual quasi-
In this paper, we show that LCD codes are not equivalent to linear codes over small finite fields. The enumeration of binary optimal LCD codes is obtained. We also get the exact value of LD$(n,2)$ over $mathbb{F}_3$ and $mathbb{F}_4$. We study the bound of LCD codes over $mathbb{F}_q$.