5 papers · 1 filter
Embedding linear codes over Z4 into self-orthogonal codes
Junmin An, Jon-Lark Kim, San Ling
The purpose of this paper is to investigate the self-orthogonal embedding problem for linear codes over Z4. We propose several tight bounds on the length of the shortest self-ortho…
Shortest LCD embeddings of binary, ternary and quaternary linear codes
Junmin An, Ji-Hoon Hong, Jon-Lark Kim +1
In the recent years, there has been active research on self-orthogonal embeddings of linear codes since they yielded some optimal self-orthogonal codes. LCD codes have a trivial hu…
New bounds for codes over Gaussian integers based on the Mannheim distance
Minjia Shi, Xuan Wang, Junmin An +1
We study linear codes over Gaussian integers equipped with the Mannheim distance. We develop Mannheim-metric analogues of several classical bounds. We derive an explicit formula fo…
Shortest self-orthogonal embeddings of binary linear codes
Junmin An, Nathan Kaplan, Jon-Lark Kim +2
There has been recent interest in the study of shortest self-orthogonal embeddings of binary linear codes, since many such codes are optimal self-orthogonal codes. Several authors…
Log-Concave Sequences in Coding Theory
Minjia Shi, Xuan Wang, Junmin An +1
We introduce the notion of logarithmically concave (or log-concave) sequences in Coding Theory. A sequence of real numbers is called log-concave if $a_i^2 \g…