PDF(474 KB)
PDF(474 KB)
PDF(474 KB)
有限域上一类负循环码
A Class of Negacyclic Codes over Finite Field
设Fq为一个阶为q的有限域，其中q为奇数.本文研究了xn+1在Fq上的不可约分解及环Fq[x]/<xn+1>中所有本原幂等元，这里的n是素因子整除q-1的某些正整数.进一步，得到了Fq上所有长度为n的不可约负循环码的检验多项式及极小汉明距离.
Let Fq be a finite field of odd order q. We study the irreducible factors of xn+1 over Fq and all primitive idempotents in the ring Fq[x]/< xn+1 >, where q -1 is divisible by the prime factors of n. Moreover, we obtain the check polynomial and the minimum Hamming distance of all irreducible negacyclic codes of length n over Fq.
不可约负循环码 / 本原幂等元 / 有限域 {{custom_keyword}} /
irreducible negacyclic code / primitive idempotent / finite field {{custom_keyword}} /
[1] Arora S. K., Pruthi M., Minimal cyclic codes of length 2pn, Finite Fields Appl., 1999, 5:177-187.
[2] Arora S. K., Batra S., Cohen S. D., et al., The primitive idempotents of a cyclic group algebra, Southeast Asian Bull. Math., 2002, 26:197-208.
[3] Arora S. K., Batra S., Cohen S. D., The primitive idempotents of a cyclic group algebra Ⅱ, Southeast Asian Bull. Math., 2005, 29:549-557.
[4] Bakshi G. K., Raka M., Minimal cyclic codes of length pnq, Finite Fields Appl., 2003, 9:432-448.
[5] Bakshi G. K., Raka M., Minimal cyclic codes of length 2m, Ranchi Univ. Math. J., 2003, 33:1-18.
[6] Chen B. C., Fan Y., Lin L., et al., Constacyclic codes over finite field, Finite Fields Appl., 2012, 18:1217-1231.
[7] Chen B. C., Li L., Tuerhong R., Explicit factorization of x2mpn-1 over finite field, Finite fields Appl., 2013, 24:95-104.
[8] Chen B. C., Liu H. W., Zhang G. H., Some minimal cyclic codes over finite field, Discrete Math., 2014, 331:142-150.
[9] Chen B. C., Liu H. W., Zhang G. H., A class of minimal cyclic codes over finite field, Des. Codes Cryptogr., 2015, 74:285-300.
[10] Lidl R., Niederreiter H., Finite Fields, Cambridge University Press, Cambridge, 2008.
[11] Li F. W., Yue Q., Li C. J., The minimum Hamming distances of irreducible cyclic codes, Finite Fields Appl., 2014, 29:225-242.
[12] Li F. W., Yue Q., Li C. J., Irreducible cyclic codes of length 4pn and 8pn, Finite fields Appl., 2015, 34:208-234.
[13] Li F., Cao X. W., A class of minimal cyclic codes over finite field, Discrete Math., 2017, 340:3197-3206.
[14] Martinez F. E. B., Vergara C. R. G., Oliveira L. B. D., Explicit factorization of xn-1∈Fq[x], Des. Codes Cryptogr., 2015, 77(1):277-286.
[15] Pruthi M., Arora S. K., Minimal codes of prime-power length, Finite Fields Appl., 1997, 3:99-113.
[16] Zanten A. J., Bojilov A., Dodunekov S. M., Generalized residue and t-residue codes and their idempotent generators, Des. Codes Cryptogr., 2015, 75(2):315-334.
国家自然科学基金资助项目（11771007，61572027）；中央高校基本科研业务资金资助项目；南京航空航天大学研究生创新基地（实验室）开放基金资助项目（kfjj20160802）
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