Open Access( n , n ( n − 1), n − 1) Permutation codes based on packing and Mendelsohn designs
Author(s) -
Peng Li
Publication year - 2016
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
ISSN - 1350-911X
DOI - 10.1049/el.2016.2403
Subject(s) - combinatorics , permutation (music) , mathematics , permutation group , binary number , permutation matrix , cyclic permutation , discrete mathematics , symmetric group , arithmetic , physics , circulant matrix , acoustics
Mendelsohn design was first used to construct n − 1 blocks of one optimal 2−( n , n , 2) packing which is isomorphic to an ( n , n − 1, n − 1) permutation array. The n ‐ary shift register (SR) formed by a group of k binary SRs of length n was constructed and then used to operate n − 1 blocks of the 2−( n , n , 2) packing which can generate n ( n − 1) blocks of another optimal 2−( n , n , 2 n ) packing from which a family of ( n , n ( n − 1), n − 1) permutation codes can be constructed.