A Large Class of <I>p</I>-Ary Cyclic Codes and Sequence Families

Zhengchun ZHOU; Xiaohu TANG; Udaya PARAMPALLI

doi:10.1587/transfun.E93.A.2272

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

Zhengchun ZHOU, Xiaohu TANG, Udaya PARAMPALLI

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Let n,k,e,m be positive integers such that n≥ 3, 1 ≤ k ≤ n-1, gcd(n,k)=e, and m= 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 ≤ l ≤ 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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.11 pp.2272-2277

Publication Date: 2010/11/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E93.A.2272

Type of Manuscript: Special Section PAPER (Special Section on Signal Design and its Application in Communications)

Category: Sequences

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Zhengchun ZHOU, Xiaohu TANG, Udaya PARAMPALLI, "A Large Class of p-Ary Cyclic Codes and Sequence Families" in IEICE TRANSACTIONS on Fundamentals, vol. E93-A, no. 11, pp. 2272-2277, November 2010, doi: 10.1587/transfun.E93.A.2272.
Abstract: Let n,k,e,m be positive integers such that n≥ 3, 1 ≤ k ≤ n-1, gcd(n,k)=e, and m= 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 ≤ l ≤ 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.2272/_p

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@ARTICLE{e93-a_11_2272,
author={Zhengchun ZHOU, Xiaohu TANG, Udaya PARAMPALLI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Large Class of p-Ary Cyclic Codes and Sequence Families},
year={2010},
volume={E93-A},
number={11},
pages={2272-2277},
abstract={Let n,k,e,m be positive integers such that n≥ 3, 1 ≤ k ≤ n-1, gcd(n,k)=e, and m= 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 ≤ l ≤ 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.},
keywords={},
doi={10.1587/transfun.E93.A.2272},
ISSN={1745-1337},
month={November},}

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TY - JOUR
TI - A Large Class of p-Ary Cyclic Codes and Sequence Families
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2272
EP - 2277
AU - Zhengchun ZHOU
AU - Xiaohu TANG
AU - Udaya PARAMPALLI
PY - 2010
DO - 10.1587/transfun.E93.A.2272
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2010
AB - Let n,k,e,m be positive integers such that n≥ 3, 1 ≤ k ≤ n-1, gcd(n,k)=e, and m= 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 ≤ l ≤ 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.
ER -