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Z_(16)环上的二次剩余码 被引量：2

Quadratic Residue Code over Z_(16)
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摘要 本文研究了整数环模16剩余类环Z16上的二次剩余码,讨论了它们的幂等生成元及其扩展码的自对偶性等代数性质,并研究了码长为7的Z16二次剩余码在两种已有的Gray映射下的有趣性质,尤其是确定了它们的Lee重量分布. In this paper, we study quadratic residue （QR） codes over integral ring mod 16 residue class ring Z16, and discuss their algebra properties, including their generator and the self-duality of their extended codes, etc. We also investigate some interesting properties of Z16-QR codes of length 7 under two kinds of Gray maps, and especially study their Lee weight distribution.
作者 谭晓青
机构地区 暨南大学数学系
出处 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2005年第4期739-748,共10页 数学研究与评论（英文版）
关键词 二次剩余码 幂等生成元 GRAY映射 Hamming重量 Lee重量. quadratic residue code idempotent generator Gray map Hamming weight Lee weight.
分类号 O157.4 [理学—基础数学]
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参考文献11

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同被引文献18

  • 1谭晓青.多项式剩余类环Z_(2m)[x]/(x^p-1)上的幂等元[J].暨南大学学报（自然科学与医学版）,2006,27(3):356-362. 被引量：1
  • 2HAMMONS A R, KUMAR P V, CALDERBANK A R, etal. The Z4-1inearity of Kerdock, Preparata, Goethals,and related codes [J]. IEEE Trans Inform Theory,1994, 40(2):301-319.
  • 3NECHAEV A A. Kerdock code in a cyclic form[J]. Dis- crete Math Appl, 1991,1 (4) :365-368.
  • 4BONNECAZE A, SOLE P, CALDERBANK A R. Qua- ternary quadratic residue codes and unimodular lattices [J]. IEEE Trans Inform Theory, 1995, 41 (2):366-377.
  • 5PLESSV S, QIAN Zhong-qing. Cyclic codes and quad- ratic residue codes over Z4 [J]. IEEE Trans Inform Theo- ry, 1996,142 (5) :1594-1600.
  • 6CHIU M H, STEPHEN S T, Yau Yung Yu. Zs-Cyclic codes and quadratic residue codes [J]. Advance in Ap- plied Mathematics, 2000, 25 (1) : 12-33.
  • 7KANWAR P. Quadratic residue codes over the integers modulo qm [J]. Contemp Math, 2000,259 : 299-312.
  • 8CALDERBANK AR., SLOANE N J A. Modular andp-adic cyclic codes[J]. Des Codes Cyptogr, 1995, 6(1) :21-35.
  • 9Macwilliams F J, Sloane N J A. The theory of error correcting codes[M]. Amsterdam, the Netherlands: North-Holland, 1977:480-520.
  • 10Pless V S. Thtroduction to the theory of error-correcting codes[M]. New York: .John Wiley, 1989:76-95.

引证文献2

二级引证文献1

Journal of Mathematical Research and Exposition
2005年 第4期

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