Two-tuple balance of non-binary sequences with ideal two-level autocorrelation

Guang Gong, Hong Yeop Song

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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 languageEnglish
Pages (from-to)2590-2598
Number of pages9
JournalDiscrete Applied Mathematics
Issue number18
Publication statusPublished - 2006 Dec 1

Bibliographical note

Funding Information:
One of Authors Guang Gong wishes to acknowledge the support of NSERC Grant RG-PIN 227700-00.

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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