Optimal Tight Equi‐Difference Conflict‐Avoiding Codes of Length n = 2k ± 1 and Weight 3 |
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| Authors: | Shung‐Liang Wu Hung‐Lin Fu |
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| Institution: | 1. Department of Computer Science and Information Engineering, National United University, , Miaoli, 36003 Taiwan;2. Department of Applied Mathematics, National Chaio Tung University, , Hsin Chu, 30010 Taiwan |
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| Abstract: | For a k‐subset X of  , the set of differences on X is the set  (mod n):  . A conflict‐avoiding code CAC of length n and weight k is a collection  of k‐subsets of  such that  = ? for any distinct  . Let CAC( ) be the class of all the CACs of length n and weight k. The maximum size of codes in CAC(n, k) is denoted by  . A code  CAC(n, k) is said to be optimal if  =  . An optimal code  is tight equi‐difference if  =  and each codeword in  is of the form  . In this paper, the necessary and sufficient conditions for the existence problem of optimal tight equi‐difference conflict‐avoiding codes of length n =  and weight 3 are given. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 21: 223–231, 2013 |
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| Keywords: | conflict‐avoiding codes equi‐difference optimal codes |
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