Factorization of X2m-1 over Z(2m-1)k
Received date: 2018-04-09
Online published: 2018-05-23
研究多项式 X2m-1 在环 Z(2m-1)k 上的不可约因式分解,其中 2m-1 为素数,并给出 X2m-1 不可约因式系数之间的约束关系,以及 m=4、6 时 X2m-1-1 的不可约因式分解。
关键词： Dickson 多项式; 因式分解; Hensel 引理
杨建生, 孙亚南 . 多项式 X2m-1 在环 Z(2m-1)k上的因式分解[J]. 上海大学学报(自然科学版), 2020 , 26(4) : 662 -670 . DOI: 10.12066/j.issn.1007-2861.2053
This paper mainly studies the factorization ofX2m-1 over Z(2m-1)k, and it obtains the constrained relationship between coefficients of irreducible factors of X2m-1
Key words： Dickson polynomial; factorization; Hensel's lemma
| [1] | MacWillianms F J, Sloane N J A. The theory of error-correcting codes [M]. The Netherlands: North-Holland Publishing Co., 1977. |
| [2] | Ling S, Sole P. Good self-dual quasi-cyclic codes exist[J]. IEEE Transactions on Information Theory, 2003,49(4):1052-1053. |
| [3] | Stichtenoth H, Topuzoglu A. Factorization of a class of polynomials over finite fields[J]. Finite Field and Their Applications, 2012,18(1):108-122. |
| [4] | Conan J, Seguin G. Structrual properties and enumeration of quasi-cyclic codes[J]. Applicable Algebra in Engineering, Communication and Computing, 1993,4(1):25-39. |
| [5] | Ling S, Sole P. On the algebraic structure of quasi-cyclic codes Ⅰ: finite fields[J]. IEEE Trans Inform Theory, 2001,47(7):2751-2760. |
| [6] | Ling S, Sole P. On the algebraic structure of quasi-cyclic code Ⅱ: chain rings[J]. Designs, Codes and Cryptography, 2003,30(1):113-130. |
| [7] | Mullen G L, Panarlo D. Handbook of finite fields [M]. Boca Raton: CRC Press, 2013: 53-99. |
| [8] | Huffman W C, Pless V. Fundamentals of error-correcting codes [M]. London: Cambridge University Press, 2003: 122-162. |
| [9] | Flori J P, Mesnager S. Dickson polynomials, hyperelliptic curves and hyper-bentfunctions[M]. New York: Springer-Verlag , 2012: 40-52. |
| [10] | Wan Z X. Finite fields and galois rings [M]. Singapore: World Scientific Publishing Co. Pte Ltd, 2003. |
/
| 〈 |
|
〉 |
