Cross-Correlation Distribution of p-Ary m-Sequence and Its p + 1 Decimated Sequences with Shorter Period

Eun-Young SEO; Young-Sik KIM; Jong-Seon NO; Dong-Joon SHIN

doi:10.1093/ietfec/e90-a.11.2568

Cross-Correlation Distribution of p-Ary m-Sequence and Its p + 1 Decimated Sequences with Shorter Period

Eun-Young SEO, Young-Sik KIM, Jong-Seon NO, Dong-Joon SHIN

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In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p + 1 distinct decimated sequences s(dt + l) is derived. For an odd prime p, an even integer n, and d = p^k +1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 ≤ l < p + 1, for a p-ary m-sequence s(t) of period pⁿ -1 because gcd(d, pⁿ - 1) = p + 1. The maximum magnitude of their cross-correlation values is 1 + p if l ≡ 0 mod p + 1 for n ≡ 0 mod 4 or l ≡ (p + 1)/2 mod p + 1 for n ≡ 2 mod 4 and otherwise, 1 + . Also by using s(t) and s(dt + l), a new family of p-ary sequences of period pⁿ -1 is constructed, whose family size is pⁿ and C_max is 1 + p.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.11 pp.2568-2574

Publication Date: 2007/11/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e90-a.11.2568

Type of Manuscript: PAPER

Category: Spread Spectrum Technologies and Applications

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Eun-Young SEO, Young-Sik KIM, Jong-Seon NO, Dong-Joon SHIN, "Cross-Correlation Distribution of p-Ary m-Sequence and Its p + 1 Decimated Sequences with Shorter Period" in IEICE TRANSACTIONS on Fundamentals, vol. E90-A, no. 11, pp. 2568-2574, November 2007, doi: 10.1093/ietfec/e90-a.11.2568.
Abstract: In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p + 1 distinct decimated sequences s(dt + l) is derived. For an odd prime p, an even integer n, and d = p^k +1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 ≤ l < p + 1, for a p-ary m-sequence s(t) of period pⁿ -1 because gcd(d, pⁿ - 1) = p + 1. The maximum magnitude of their cross-correlation values is 1 + p if l ≡ 0 mod p + 1 for n ≡ 0 mod 4 or l ≡ (p + 1)/2 mod p + 1 for n ≡ 2 mod 4 and otherwise, 1 + . Also by using s(t) and s(dt + l), a new family of p-ary sequences of period pⁿ -1 is constructed, whose family size is pⁿ and C_max is 1 + p.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.11.2568/_p

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@ARTICLE{e90-a_11_2568,
author={Eun-Young SEO, Young-Sik KIM, Jong-Seon NO, Dong-Joon SHIN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Cross-Correlation Distribution of p-Ary m-Sequence and Its p + 1 Decimated Sequences with Shorter Period},
year={2007},
volume={E90-A},
number={11},
pages={2568-2574},
abstract={In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p + 1 distinct decimated sequences s(dt + l) is derived. For an odd prime p, an even integer n, and d = p^k +1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 ≤ l < p + 1, for a p-ary m-sequence s(t) of period pⁿ -1 because gcd(d, pⁿ - 1) = p + 1. The maximum magnitude of their cross-correlation values is 1 + p if l ≡ 0 mod p + 1 for n ≡ 0 mod 4 or l ≡ (p + 1)/2 mod p + 1 for n ≡ 2 mod 4 and otherwise, 1 + . Also by using s(t) and s(dt + l), a new family of p-ary sequences of period pⁿ -1 is constructed, whose family size is pⁿ and C_max is 1 + p.},
keywords={},
doi={10.1093/ietfec/e90-a.11.2568},
ISSN={1745-1337},
month={November},}

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TY - JOUR
TI - Cross-Correlation Distribution of p-Ary m-Sequence and Its p + 1 Decimated Sequences with Shorter Period
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2568
EP - 2574
AU - Eun-Young SEO
AU - Young-Sik KIM
AU - Jong-Seon NO
AU - Dong-Joon SHIN
PY - 2007
DO - 10.1093/ietfec/e90-a.11.2568
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2007
AB - In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p + 1 distinct decimated sequences s(dt + l) is derived. For an odd prime p, an even integer n, and d = p^k +1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 ≤ l < p + 1, for a p-ary m-sequence s(t) of period pⁿ -1 because gcd(d, pⁿ - 1) = p + 1. The maximum magnitude of their cross-correlation values is 1 + p if l ≡ 0 mod p + 1 for n ≡ 0 mod 4 or l ≡ (p + 1)/2 mod p + 1 for n ≡ 2 mod 4 and otherwise, 1 + . Also by using s(t) and s(dt + l), a new family of p-ary sequences of period pⁿ -1 is constructed, whose family size is pⁿ and C_max is 1 + p.
ER -