Necessary and sufficient conditions for tight equi-difference conflict-avoiding codes of weight three |
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Authors: | Koji Momihara |
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Affiliation: | (1) Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku 464-8601, Japan |
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Abstract: | A conflict-avoiding code (CAC) C of length n and weight k is a collection of k-subsets of such that holds for any , , where . A CAC with maximum code size for given n and k is called optimal. Furthermore, an optimal CAC C is said to be tight equi-difference if holds and any codeword has the form . The concept of a CAC is motivated from applications in multiple-access communication systems. In this paper, we give a necessary and sufficient condition to construct tight equi-difference CACs of weight k = 3 and characterize the code length n’s admitting the condition through a number theoretical approach. |
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Keywords: | Tight equi-difference conflict-avoiding codes 2 r -th power residue Kronecker density |
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