10 papers
Embedding Linear Codes into Optimal Self-Orthogonal Codes Based on Constraint-Preserving Genetic Algorithms
Haeun Lim, Junmin An, Jon-Lark Kim
We study the problem of finding shortest self-orthogonal embeddings of a given code which have the largest possible minimum distance by employing a constraint-preserving genetic al…
New binary optimal LCD codes using heuristic embedding
Haeun Lim, Junmin An, Jon-Lark Kim
In this paper, we investigate the construction of binary optimal LCD codes through short LCD embeddings. For this purpose, we design heuristic frameworks based on a greedy algorith…
Shortest self-orthogonal and LCD embeddings of linear codes over Fq+uFq
Junmin An, Jon-Lark Kim
This paper determines the exact lengths of shortest self-orthogonal and LCD embeddings of linear codes over . By decomposing Gram matrices over $\mathbb…
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…
Symmetric Sudoku-Type Games from Perfect Codes
Junmin An, Jae-Hyun Baek, Keon-Hwi Kim +2
This paper presents a novel construction method for symmetric Sudoku-type games based on Lee distance perfect codes and diameter perfect codes. The proposed method utilizes the til…
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 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…
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…
The Dimensions of the Hulls of Conorm Codes from Algebraic Geometry Codes
Junmin An, Jon-Lark Kim
Chara et al. introduced conorm codes defined over algebraic geometry codes, but the hulls of conorm codes were not determined yet. In this paper, we study the dimension of the hull…