AN IDENTITY BETWEEN THE m-SPOTTY ROSENBLOOM-TSFASMAN WEIGHT ENUMERATORS OVER FINITE COMMUTATIVE FROBENIUS RINGS

다국어 초록 (Multilingual Abstract)

This paper is devoted to presenting a MacWilliams type identity for m-spotty RT weight enumerators of byte error control codes over finite commutative Frobenius rings, which can be used to determine the error-detecting and error-correcting capabilities of a code. This provides the relation between the m-spotty RT weight enumerator of the code and that of the dual code. We conclude the paper by giving three illustrations of the results.

참고문헌 (Reference)

1 F. J. MacWilliams, "The Theory of Error-Correcting Codes" North-Holland Publishing Company 1978

2 M. ¨Ozen, "The MacWilliams identity for m-spotty weight enumerators of linear codes over finite fields" 61 (61): 1000-1004, 2011

3 M. ¨Ozen, "The MacWilliams identity for m-spotty Rosenbloom-Tsfasman weight enumer-ator" 351 (351): 743-750, 2014

4 A. Sharma, "On some new m-spotty Lee weight enumerators" 71 (71): 119-152, 2014

5 A. Sharma, "On MacWilliams type identities for r-fold joint m-spotty weight enumerators" 312 (312): 3316-3327, 2012

6 B. C. Chen, "Matrix product codes with Rosenbloom-Tsfasman metric" 33 (33): 687-700, 2013

7 Y. Fan, "Matrix product codes over finite commutative Frobenius rings" 71 (71): 201-227, 2014

8 A. Sharma, "MacWilliams type identities for some new m-spotty weight enumerators" 58 (58): 3912-3924, 2012

9 K. Suzuki, "MacWilliams identity for m-spotty weight enumerator" E93-A (E93-A): 526-531, 2010

10 M. J. Shi, "MacWilliams identity for m-spotty Lee weight enumerators over F2 + uF2 + · · · + um−1F2"

11 I. Siap, "MacWilliams identity for m-spotty Lee weight enumerators" 23 (23): 13-16, 2010

12 K. Q. Feng, "Linear error-block codes" 12 (12): 638-652, 2006

13 J. Wood, "Duality for modules over finite rings and application to coding theory" 121 (121): 555-575, 1999

14 S. T. Dougherty, "Codes over Rk, Gray maps and their binary images" 17 (17): 205-219, 2011

15 M. ¨Ozen, "Codes over Galois rings with respect to the Rosenbloom-Tsfasman metric" 344 (344): 790-799, 2007

16 M. Y. Rosenbloom, "Codes for the m-metric" 33 (33): 45-52, 1997

17 E. Fujiwara, "Code Design for Dependable System: Theory and Practical Applications" Wiley & Son, Inc 2006

18 L. Panek, "Classification of Niederreiter-Rosenbloom-Tsfasman block codes" 56 (56): 5207-5216, 2010

19 I. Siap, "An identity between the m-spotty weight enumerators of a linear code and its dual" 36 (36): 641-650, 2012

20 K. Suzuki, "A general class of m-spotty weight enumer-ator" E90-A (E90-A): 1418-1427, 2007

21 G. Umanesan, "A class of random multiple bits in a byte error correcting and single byte error detecting (St/bEC-SbED) codes" 52 (52): 835-847, 2003

22 V. S¸iap, "A MacWilliams Type identity for m-spotty Rosenbloom-Tsfasman weight enumerators over Frobenius rings" 1236-1241, 2013