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)

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]

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]

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

New good large (n,r)-arcs in PG(2,29) and PG(2,31)

An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximumsize of an $(n, r)$-arc in \PG(2,q) is denoted by $m_r(2,q)$. In this article a $(477, 18)$-arc, a $(596,22)$-arc, a $(697,25)$-arc in PG(2,29) and a $(598, 21)$-arc, a $(664, 23)$-arc, a $(699, 24)$-arc, a $(769, 26)$-arc, a $(838,28)$-arc in PG(2,31) are presented. The constructed arcs improve the respective lower bounds on $m_r(2,29)$ and $m_r(2,31)$ in \cite{MB2019}. As a consequence there exist eight new three-dimensional linear codes over the respective finite fields.\

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]