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We derive Singleton-type bounds on the free distance and column distances of trellis codes. Our results show that, at a given time instant, the maximum attainable column distance of trellis codes can exceed that of convolutional codes.…
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…
In this paper, we provide a polynomial characterization of linear complementary pairs of quasi-cyclic and quasi-twisted codes of index 2. We also give several examples of linear complementary pairs of quasi-cyclic and quasi-twisted codes…
Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given $n$ and $r<n$, with $n$ or $r$ (or both) odd, MDS LCD $(n,r)$ codes are constructed over finite fields whose…
Additive conjucyclic codes over $\F_{q^2}$ are closed under the conjugated cyclic shift and play an important role in constructing quantum error-correcting codes (QECCs). However, a systematic algebraic theory for such codes over general…
Certain simplicial complexes are used to construct a subset $D$ of $\mathbb{F}_{2^n}^m$ and $D$, in turn, defines the linear code $C_{D}$ over $\mathbb{F}_{2^n}$ that consists of $(v\cdot d)_{d\in D}$ for $v\in \mathbb{F}_{2^n}^m$. Here we…
Spectral bounds form a powerful tool to estimate the minimum distances of quasi-cyclic codes. They generalize the defining set bounds of cyclic codes to those of quasi-cyclic codes. Based on the eigenvalues of quasi-cyclic codes and the…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
We study quasi-cyclic codes of index 2 over finite fields. We give a classification of such codes. Their duals with respect to the Euclidean, symplectic and Hermitian inner products are investigated. We describe self-orthogonal and…
A linear code with parameters $[n, k, n - k + 1]$ is called maximum distance separable (MDS), and one with parameters $[n, k, n - k]$ is called almost MDS (AMDS). A code is near-MDS (NMDS) if both it and its dual are AMDS. NMDS codes…
Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…
In this paper, we investigate the structure and properties of additive complementary dual (ACD) codes over the mixed alphabet $\mathbb{F}_2\mathbb{F}_4$ relative to a certain inner product defined over $\mathbb{F}_2\mathbb{F}_4$. We…
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in…
LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are…
This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant…
Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic…
This paper deals with the problem of increasing the minimum distance of a linear code by adding one or more columns to the generator matrix. Several methods to compute extensions of linear codes are presented. Many codes improving the…
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…
The class of 1-generator quasi-abelian codes over finite fields is revisited. Alternative and explicit characterization and enumeration of such codes are given. An algorithm to find all 1-generator quasi-abelian codes is provided. Two…
In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction…