MacWilliams Identity for Codes with the Rank Metric
نویسندگان
چکیده
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.
منابع مشابه
MacWilliams Identity for Codes with the Hamming and Rank Metrics
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 first provide an alternative proof to the MacWilliams identity for linear codes with the Hamming metric. An intermediate result of our approach is that the Hamming weight enumerator of the dual of any ...
متن کاملMacWilliams Identity for Rank Metric Codes
In this paper, we study the rank distributions of linear codes. We give the analogous to the MacWilliams identity for the rank distributions of codes. The considerations of our proof can be adapted to give an alternate derivation of the identity for the Hamming metric. This derivation does not rely on the identity for the complete weight enumerator. Using the result for the rank metric, we dete...
متن کاملRank-metric codes and their duality theory
We compare the two duality theories of rank-metric codes proposed by Delsarte and Gabidulin, proving that the former generalizes the latter. We also give an elementary proof of MacWilliams identities for the general case of Delsarte rank-metric codes, in a form that never appeared in the literature. The identities which we derive are very easy to handle, and allow us to re-establish in a very c...
متن کاملProperties of Rank Metric Codes
This paper investigates general properties of codes with the rank metric. First, we investigate asymptotic packing properties of rank metric codes. Then, we study sphere covering properties of rank metric codes, derive bounds on their parameters, and investigate their asymptotic covering properties. Finally, we establish several identities that relate the rank weight distribution of a linear co...
متن کاملCodes Endowed With the Rank Metric
We review the main results of the theory of rank-metric codes, with emphasis on their combinatorial properties. We study their duality theory and MacWilliams identities, comparing in particular rank-metric codes in vector and matrix representation. We then investigate the combinatorial structure of MRD codes and optimal anticodes in the rank metric, describing how they relate to each other.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- EURASIP J. Wireless Comm. and Networking
دوره 2008 شماره
صفحات -
تاریخ انتشار 2008