Some new quasi-twisted ternary linear codes

Let $[n,k,d]_q$ code be a linear code of length $n$, dimension $k$ and minimum Hamming distance $d$ over $GF(q)$. One of the basic and most important problems in coding theory is to construct codes with best possible minimum distances. In this paper seven quasi-twisted ternary linear codes are constructed. These codes are new and improve the best known lower bounds on the minimum distance in [6]

Some new ternary linear codes

Let an $[n,k,d]_q$ code be a linear code of length $n$, dimension $k$ and minimum Hamming distance $d$ over $GF(q)$. One of the most important problems in coding theory is to construct codes with optimal minimum distances. In this paper 22 new ternary linear codes are presented. Two of them are optimal. All new codes improve the respective lower bounds in [11]

Generating generalized necklaces and new quasi-cyclic codes

In many cases there is a need of exhaustive lists of combinatorial objects of a given type. We consider generation of all inequivalent polynomials from which defining polynomials for constructing quasi-cyclic (QC) codes are to be chosen. Using these defining polynomials we construct 34 new good QC codes over GF(11) and 36 such codes over GF(13)

New minimum distance bounds for linear codes over GF(5)

AbstractLet [n,k,d]q-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). In this paper, 32 new codes over GF(5) are constructed and the nonexistence of 51 codes is proved

Construction of Quasi-Twisted Codes and Enumeration of Defining Polynomials

Let $d_{q}(n,k)$ be the maximum possible minimum Hamming distance of a linear [$n,k$] code over \F_{q}. Tables of best known linear codes exist for small fields and some results are known for larger fields. Quasi-twisted codes are constructed using $m \times m$ twistulant matrices and many of these are the best known codes. In this paper, the number of $m \times m$ twistulant matrices over \FF_q is enumerated and linear codes over \F_{17} and \F_{19} are constructed for $k$ up to $5$