( n ,  n ( n  − 1),  n  − 1) Permutation codes based on packing and Mendelsohn designs | Zendy

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( 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.

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