Recently linear codes with respect to the Poset metric have been studied intensively. Poset metric includes the well-known Hamming and Rosenbloom-Tsfasman metrics as special cases. Here, we define an alternative P-complete weight enumerator of linear codes with respect to poset metric. We establish a MacWilliams identity and conclude with an illustrative example.
R. A. Brualdi, J. Graves, K. M. Lawrence, Codes with a poset metric, Disc. Math., Dec. , 147, 57. F. J. MacWilliams, N. J. Sloane, The Theory of Error- Correcting Codes, Amsterdam, The Netherlands: North- Holland, 1977.
H.K. Kim, D.Y. Oh, A Classification of Posets Admitting the MacWilliams Identity, IEEE, 2005, 51, 1424.
S. Ling, C. Xing, Coding Theory A First Course. National University of Singapore, Cambridge University Pres, 2004.
W.C. Huffman, V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, 2003.
M. Firer, L. Panek, L. Rifo, Coding in the Presence of Semantic Value of Information: Unequal Error Protection Using Poset Decoders, arXiv: 1102.3832v1, 17 Aug 2011.
Poset Metriği İçin P-Tam Ağırlık Sayacı ve MacWilliams Özdeşliği
Son zamanlarda ağırlıklı olarak poset metriğine bağlı lineer kodlar çalışılmaktadır. Poset metriği özel hal olarak iyi bilinen Hamming ile Rosenbloom-Tsfasman metriklerini içerir. Bu makalede, poset metriğine bağlı alternatif bir P-tam ağırlık sayacı tanımlanmaktadır. MacWilliams Özdeşliği ispat edilmekte ve aydınlatıcı bir örnek verilmektedir.
R. A. Brualdi, J. Graves, K. M. Lawrence, Codes with a poset metric, Disc. Math., Dec. , 147, 57. F. J. MacWilliams, N. J. Sloane, The Theory of Error- Correcting Codes, Amsterdam, The Netherlands: North- Holland, 1977.
H.K. Kim, D.Y. Oh, A Classification of Posets Admitting the MacWilliams Identity, IEEE, 2005, 51, 1424.
S. Ling, C. Xing, Coding Theory A First Course. National University of Singapore, Cambridge University Pres, 2004.
W.C. Huffman, V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, 2003.
M. Firer, L. Panek, L. Rifo, Coding in the Presence of Semantic Value of Information: Unequal Error Protection Using Poset Decoders, arXiv: 1102.3832v1, 17 Aug 2011.
Şiap, İ., Akbıyık, S., & Akbıyık, S. (2011). Poset Metriği İçin P-Tam Ağırlık Sayacı ve MacWilliams Özdeşliği. Adıyaman University Journal of Educational Sciences, 1(1), 28-39.