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Optimal doubly constant weight codes
Author(s) -
Etzion Tuvi
Publication year - 2008
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20160
Subject(s) - mathematics , combinatorics , steiner system , constant (computer programming) , generalization , code word , minimum weight , discrete mathematics , code (set theory) , combinatorial design , minimum distance , decoding methods , algorithm , set (abstract data type) , computer science , mathematical analysis , programming language
Abstract A doubly constant weight code is a binary code of length n 1 + n 2 , with constant weight w 1 + w 2 , such that the weight of a codeword in the first n 1 coordinates is w 1 . Such codes have applications in obtaining bounds on the sizes of constant weight codes with given minimum distance. Lower and upper bounds on the sizes of such codes are derived. In particular, we show tight connections between optimal codes and some known designs such as Howell designs, Kirkman squares, orthogonal arrays, Steiner systems, and large sets of Steiner systems. These optimal codes are natural generalization of Steiner systems and they are also called doubly Steiner systems. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 137–151, 2008