Notes on Linear Codes over Finite Commutative Chain Rings
Notes on Linear Codes over Finite Commutative Chain Rings
摘要
The properties of the generator matrix are given for linear codes over finite commutative chain rings, and the so-called almost-MDS (AMDS) codes are studied.
The properties of the generator matrix are given for linear codes over finite commutative chain rings, and the so-called almost-MDS (AMDS) codes are studied.
基金
Supported by the National Natural Science Foundation of China (No. 60402022)
参考文献11
-
1Byrne, E., Greferath, M., Honold, T. Ring geometries, two-weight codes, and strongly regular graphs. Des. Codes Cryptogr., 48(1): 1-16 (2008).
-
2Dinh, H.Q., Lopez-Permouth, S.R. Cyclic and negacyclic codes over finite chain rings. IEEE Trans. Inform. Theory, 50(8): 1728-1744 (2004).
-
3Hammons, A.R., Kumar, P.V., Calderbank, A.R., Sloane, N.J.A., Sole, P. The Z4-1inearity of Kerdock, Preparata, Goethals and related codes. IEEE Trans. Inform. Theory, 40(2): 301-319 (1994).
-
4Horimoto. H., 3hiromoto, K. On generalized Hamming weights for codes over finite chain rings. In: Proceedings of the 14th International Symposium on Applied Algebra. Algebraic Algorithms and Error- Correcting Codes, Springer-Verlag, Berlin, Heidelberg, 2001. 141-150.
-
5Liu, Z.H. The weight hierarchy of linear codes. Ph.D. Dissertation, Chinese Academy of Sciences, Beijing, 2003 (in Chinese).
-
6McDonald, B.R. Linear algebra over commutative rings. Marcel Dekker, New York, 1984.
-
7Shiromoto, K., Storme, L. A Griesmer bound for linear codes over finite quasi-Frobenius rings. Discrete Applied Mathematics, 128(1): 263-274 (2003).
-
8Wei, V.K. Generalized Hamming weight for linear codes. IEEE Trans. Inform. Theory, 37(5): 1412-1418 (1991).
-
9Wei, V.K., Yang, K. On the generalized Hamming weight of product codes. IEEE Trans. Inform. Theory, 39(5): 1709 1713 (1993).
-
10Wood, J.A. Duality for modules over finite rings and applications to coding theory. American journal of Mathematics, 121(3): 555-575 (1999).
-
1张光辉.关于有限链环上自对偶循环码的注记(英文)[J].数学进展,2016,45(2):206-210. 被引量:1
-
2张荔,薛海波.可表示成3个真子群并的群[J].太原师范学院学报(自然科学版),2008,7(3):43-44. 被引量:1
-
3朱用文.有限交换幺环的自同态[J].烟台大学学报(自然科学与工程版),2001,14(1):11-14. 被引量:1
-
4LIU Xiusheng,LIU Hualu.Macwilliams Identities of Linear Codes over the Ring F_2+ uF_2+ vF_2[J].Journal of Systems Science & Complexity,2015,28(3):691-701.
-
5赵健伟.“诺贝尔奖综合征”再度复发[J].语文新圃,2009(11):4-5.
-
6高莹.BILINEAR FORMS AND LINEAR CODES[J].Acta Mathematica Scientia,2004,24(1):100-106.
-
7陈芳,陈滋利.Notes on Preregular Operators in Banach Lattices[J].Journal of Southwest Jiaotong University(English Edition),2009,17(4):363-365.
-
8LIU Zihui,CHEN Wende.Weight hierarchies of linear codes satisfying the Near-Chain condition[J].Progress in Natural Science:Materials International,2005,15(9):784-792.
-
9Shixin ZHU,Yongsheng TANG.A MACWILLIAMS TYPE IDENTITY ON LEE WEIGHT FOR LINEAR CODES OVER F_2+uF_2[J].Journal of Systems Science & Complexity,2012,25(1):186-194. 被引量:3
-
10简岩.如何根治“统一休假综合征”[J].百科知识,2012(21):1-1.