Abstract
Let p be a prime, q = pm and Fq be the finite field with q elements. In this paper, we will consider q-ary sequences of period qn - 1 for q > 2 and study their various balance properties: symbol-balance, difference-balance, and two-tuple-balance properties. The array structure of the sequences is introduced, and various implications between these balance properties and the array structure are proved. Specifically, we prove that if a q-ary sequence of period qn - 1 is difference-balanced and has the "cyclic" array structure then it is two-tuple-balanced. We conjecture that a difference-balanced q-ary sequence of period qn - 1 must have the cyclic array structure. The conjecture is confirmed with respect to all of the known q-ary sequences which are difference-balanced, in particular, which have the ideal two-level autocorrelation function when q = p.
| Original language | English |
|---|---|
| Pages (from-to) | 2590-2598 |
| Number of pages | 9 |
| Journal | Discrete Applied Mathematics |
| Volume | 154 |
| Issue number | 18 |
| DOIs | |
| Publication status | Published - 2006 Dec 1 |
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All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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Two-tuple balance of non-binary sequences with ideal two-level autocorrelation. / Gong, Guang; Song, Hong Yeop.
In: Discrete Applied Mathematics, Vol. 154, No. 18, 01.12.2006, p. 2590-2598.Research output: Contribution to journal › Article
TY - JOUR
T1 - Two-tuple balance of non-binary sequences with ideal two-level autocorrelation
AU - Gong, Guang
AU - Song, Hong Yeop
PY - 2006/12/1
Y1 - 2006/12/1
N2 - Let p be a prime, q = pm and Fq be the finite field with q elements. In this paper, we will consider q-ary sequences of period qn - 1 for q > 2 and study their various balance properties: symbol-balance, difference-balance, and two-tuple-balance properties. The array structure of the sequences is introduced, and various implications between these balance properties and the array structure are proved. Specifically, we prove that if a q-ary sequence of period qn - 1 is difference-balanced and has the "cyclic" array structure then it is two-tuple-balanced. We conjecture that a difference-balanced q-ary sequence of period qn - 1 must have the cyclic array structure. The conjecture is confirmed with respect to all of the known q-ary sequences which are difference-balanced, in particular, which have the ideal two-level autocorrelation function when q = p.
AB - Let p be a prime, q = pm and Fq be the finite field with q elements. In this paper, we will consider q-ary sequences of period qn - 1 for q > 2 and study their various balance properties: symbol-balance, difference-balance, and two-tuple-balance properties. The array structure of the sequences is introduced, and various implications between these balance properties and the array structure are proved. Specifically, we prove that if a q-ary sequence of period qn - 1 is difference-balanced and has the "cyclic" array structure then it is two-tuple-balanced. We conjecture that a difference-balanced q-ary sequence of period qn - 1 must have the cyclic array structure. The conjecture is confirmed with respect to all of the known q-ary sequences which are difference-balanced, in particular, which have the ideal two-level autocorrelation function when q = p.
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UR - http://www.scopus.com/inward/citedby.url?scp=33750429950&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2006.04.025
DO - 10.1016/j.dam.2006.04.025
M3 - Article
AN - SCOPUS:33750429950
VL - 154
SP - 2590
EP - 2598
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
IS - 18
ER -