Related papers: Constructions of Quasi-Twisted Two-Weight Codes
Quasi-twisted (QT) codes are a generalization of quasi-cyclic (QC) codes. Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented. It is also shown that…
Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on…
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…
Based on cyclic simplex codes, a new construction of a family of 2-generator quasi-cyclic two-weight codes is given. New optimal binary quasi-cyclic [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, good QC ternary [195, 6, 126], [208,…
Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association…
The results of [1,2] on linear homogeneous two-weight codes over finite Frobenius rings are exended in two ways: It is shown that certain non-projective two-weight codes give rise to strongly regular graphs in the way described in [1,2].…
The results of [1,2] on linear homogeneous two-weight codes over finite Frobenius rings are exended in two ways: It is shown that certain non-projective two-weight codes give rise to strongly regular graphs in the way described in [1,2].…
Projective two-weight linear codes are closely related to finite projective spaces and strongly regular graphs. In this paper, a family of $q$-ary projective two-weight linear codes is presented, where $q$ is a power of 2. The parameters of…
It is known that a linear two-weight code $C$ over a finite field $\F_q$ corresponds both to a multiset in a projective space over $\F_q$ that meets every hyperplane in either $a$ or $b$ points for some integers $a<b$, and to a strongly…
Cyclic codes of dimension $2$ over a finite field are shown to have at most two nonzero weights. This extends a construction of Rao et al (2010) and disproves a conjecture of Schmidt-White (2002). We compute their weight distribution, and…
Inspired by the Z2Z4-additive codes, linear codes over Z2^r x(Z2+uZ2)^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z2^r x(Z2+uZ2)^s have some advantages…
This paper introduces a new combinatorial construction for q-ary constant-weight codes which yields several families of optimal codes and asymptotically optimal codes. The construction reveals intimate connection between q-ary…
Let $p$ be a prime number. Irreducible cyclic codes of length $p^2-1$ and dimension $2$ over the integers modulo $p^h$ are shown to have exactly two nonzero Hamming weights. The construction uses the Galois ring of characteristic $p^h$ and…
Quasi-twisted (QT) codes generalize several important families of linear codes, including cyclic, constacyclic, and quasi-cyclic codes. Despite their potential, to the best of our knowledge, there exists no efficient decoding algorithm for…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
Many kinds of codes which possess two cycle structures over two special finite commutative chain rings, such as ${\Bbb Z}_2{\Bbb Z}_4$-additive cyclic codes and quasi-cyclic codes of fractional index etc., were proved asymptotically good.…
In this work, our main objective is to construct quantum codes from quasi-twisted (QT) codes. At first, a necessary and sufficient condition for Hermitian self-orthogonality of QT codes is introduced by virtue of the Chinese Remainder…
Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…
We give necessary conditions for a two-weight projective cyclic code to be the direct sum of two one-weight irreducible cyclic subcodes of the same dimension, following the work of Wolfmann and Vega. This confirms Vega's conjecture that all…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…