1. New Lower Bounds for Permutation Codes Using Linear Block Codes
- Author
-
Alessandro Neri and Giacomo Micheli
- Subjects
FOS: Computer and information sciences ,Block code ,Degree (graph theory) ,Computer Science - Information Theory ,Information Theory (cs.IT) ,020206 networking & telecommunications ,Hamming distance ,02 engineering and technology ,Library and Information Sciences ,Linear code ,Computer Science Applications ,Combinatorics ,Permutation ,Parity-check matrix ,Cardinality ,Symmetric group ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,94B60, 94B65, 05A05 ,MathematicsofComputing_DISCRETEMATHEMATICS ,Information Systems ,Mathematics - Abstract
In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, using the columns of a parity check matrix of an $[n,k,d]_q$ linear block code, we are able to prove the existence of a permutation code in the symmetric group of degree $n$, having minimum distance at least $d$ and large cardinality. With our technique, we obtain new lower bounds for permutation codes that enhance the ones in the literature and provide asymptotic improvements in certain regimes of length and distance of the permutation code., Comment: 12 pages
- Published
- 2020
- Full Text
- View/download PDF