Trace representation and linear complexity of binary eth power residue sequences of period p

Zongduo Dai, Guang Gong, Hong-Yeop Song, Dingfeng Ye

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Let p = ef+1 be an odd prime for some e and f, and let Fp be the finite field with pelements. In this paper, we explicitly describe the trace representations of the binary characteristic sequences (of period p) of all the cyclic difference sets D which are some union of cosets of eth powers H e in Fp* (Δ\= Fp \{0}) for e≤ 12. For this, we define eth power residue sequences of period p, which include all the binary characteristic sequences mentioned above as special cases, and reduce the problem of determining their trace representations to that of determining the values of the generating polynomials of cosets of H e in Fp* at some primitive pth root of unity, and some properties of these values are investigated. Based on these properties, the trace representation and linear complexity not only of the characteristic sequences of all the known eth residue difference sets, but of all the sixth power residue sequences are determined. Furthermore, we have determined the linear complexity of a nonconstant eth power residue sequence for any e to be either p-1 or p whenever (e,(p-1)/n)= 1, where n is the order of 2 mod p.

Original languageEnglish
Article number5714271
Pages (from-to)1530-1547
Number of pages18
JournalIEEE Transactions on Information Theory
Volume57
Issue number3
DOIs
Publication statusPublished - 2011 Mar 1

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Polynomials
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All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Cite this

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Trace representation and linear complexity of binary eth power residue sequences of period p. / Dai, Zongduo; Gong, Guang; Song, Hong-Yeop; Ye, Dingfeng.

In: IEEE Transactions on Information Theory, Vol. 57, No. 3, 5714271, 01.03.2011, p. 1530-1547.

Research output: Contribution to journalArticle

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