Optimal doubly constant weight codes |
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| Authors: | Tuvi Etzion |
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| Institution: | Department of Computer Science, Technion—Israel Institute of Technology, Technion City, Haifa 32000, Israel |
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| Abstract: | A doubly constant weight code is a binary code of length n1 + n2, with constant weight w1 + w2, such that the weight of a codeword in the first n1 coordinates is w1. 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 |
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| Keywords: | doubly constant weight code Howell design Kirkman square large set Steiner system orthogonal array |
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