Maximum Distance Separable Codes in the ρ Metric over Arbitrary Alphabets
Steven T. Dougherty
and Maxim M. Skriganov2
2dagger
DOI: 10.1023/A:1020834531372
Abstract
We give a bound for codes over an arbitrary alphabet in a non-Hamming metric and define MDS codes as codes meeting this bound. We show that MDS codes are precisely those codes that are uniformly distributed and show that their weight enumerators based on this metric are uniquely determined.
Pages: 71–81
Keywords: MDS codes; uniform distributions
Full Text: PDF
References
1. S.T. Dougherty and K. Shiromoto, “MDR codes over Zk ,” IEEE-IT 46(1) (2000), 265-269.
2. S.T. Dougherty and M.M. Skriganov, “MacWilliams duality and the Rosenbloom-Tsfasman metric,” Moscow Mathematical Journal 2(1) (2002), 83-99.
3. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.
4. W.J. Martin and D.R. Stinson, “Association schemes for ordered orthogonal arrays and (T , M, S)-nets,” Canad. J. Math. 51 (1999), 326-346.
5. M. Yu Rosenbloom and M.A. Tsfasman, “Codes for the m-metric,” Problems of Information Transmission, 33(1) (1997), 45-52. (Translated from Problemy Peredachi Informatsii 33(1) (1996), 55-63.
6. M.M. Skriganov, “Coding theory and uniform distributions,” Algebra i Analiz 13(2) (2001), 191-239. (Translation to appear in St. Petersburg Math. J.).
2. S.T. Dougherty and M.M. Skriganov, “MacWilliams duality and the Rosenbloom-Tsfasman metric,” Moscow Mathematical Journal 2(1) (2002), 83-99.
3. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.
4. W.J. Martin and D.R. Stinson, “Association schemes for ordered orthogonal arrays and (T , M, S)-nets,” Canad. J. Math. 51 (1999), 326-346.
5. M. Yu Rosenbloom and M.A. Tsfasman, “Codes for the m-metric,” Problems of Information Transmission, 33(1) (1997), 45-52. (Translated from Problemy Peredachi Informatsii 33(1) (1996), 55-63.
6. M.M. Skriganov, “Coding theory and uniform distributions,” Algebra i Analiz 13(2) (2001), 191-239. (Translation to appear in St. Petersburg Math. J.).