A Large Class of p-Ary Cyclic Codes and Sequence Families

• ZHOU Zhengchun

  School of Mathematics, Southwest Jiaotong University Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University

• TANG Xiaohu

  Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University

• PARAMPALLI Udaya

  Department of Computer Science and Software Engineering, University of Melbourne

抄録

Let n, k, e, m be positive integers such that n ≥ 3, 1 ≤ k ≤ n - 1, gcd(n, k) = e, and $m={n\\over e}$ is odd. In this paper, for an odd prime p, we derive a lower bound for the minimal distance of a large class of p-ary cyclic codes C_l with nonzeros α^-1, α^{-(p^k+1)}, α^{-(p^3k+1)}, …, α^{-(p^(2l-1)k+1)}, where $1\\leq l\\leq {m-1\\over 2}$ and α is a primitive element of the finite field F_pⁿ. Employing these codes, p-ary sequence families with a flexible tradeoff between low correlation and large size are constructed.

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E93-A (11), 2272-2277, 2010

  一般社団法人 電子情報通信学会

キーワード

• cyclic code
• <i>p</i>-ary sequence
• quadratic form

詳細情報

• CRID: 1390001206311774848
• NII論文ID: 10027985234
• NII書誌ID: AA10826239
• DOI: 10.1587/transfun.e93.a.2272
• ISSN: 17451337
• ISSN: 09168508
• Web Site: http://www.jstage.jst.go.jp/article/transfun/E93.A/11/E93.A_11_2272/_pdf
• 本文言語コード: en
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