tailieunhanh - Báo cáo hóa học: "Research Article MacWilliams Identity for Codes with the Rank Metric"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article MacWilliams Identity for Codes with the Rank Metric | Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2008 Article ID 754021 13 pages doi 2008 754021 Research Article MacWilliams Identity for Codes with the Rank Metric Maximilien Gadouleau and Zhiyuan Yan Department of Electrical and Computer Engineering Lehigh University Bethlehem PA 18015 USA Correspondence should be addressed to Maximilien Gadouleau magc@ Received 10 November 2007 Accepted 3 March 2008 Recommended by Andrej Stefanov The MacWilliams identity which relates the weight distribution of a code to the weight distribution of its dual code is useful in determining the weight distribution of codes. In this paper we derive the MacWilliams identity for linear codes with the rank metric and our identity has a different form than that by Delsarte. Using our MacWilliams identity we also derive related identities for rank metric codes. These identities parallel the binomial and power moment identities derived for codes with the Hamming metric. Copyright 2008 M. Gadouleau and Z. Yan. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. INTRODUCTION The MacWilliams identity for codes with the Hamming metric 1 which relates the Hamming weight distribution of a code to the weight distribution of its dual code is useful in determining the Hamming weight distribution of codes. This is because if the dual code has a small number of codewords or equivalence classes of codewords under some known permutation group its weight distribution can be obtained by exhaustive examination. It also leads to other identities for the weight distribution such as the Pless identities 1 2 . Although the rank has long been known to be a metric implicitly and explicitly . see 3 the rank metric was first considered for error-control codes ECCs by Delsarte 4 . The .