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A family of nonbinary sequences with optimal correlation property. (English) Zbl 1356.94046

Summary: In this paper, we first present a family of \(p\)-ary sequences with ideal two- level autocorrelation property, which could be regarded as a generalization of the well-known nonbinary sequences introduced by T. Helleseth and G. Gong [IEEE Trans. Inf. Theory 48, No. 11, 2868–2872 (2002; Zbl 1062.94033)]. Utilizing the proposed sequences and \(m\)-sequences, we later construct a family of \(p\)-ary sequences of which the correlation property is optimal in terms of the Welch lower bound.

MSC:

94A55 Shift register sequences and sequences over finite alphabets in information and communication theory
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)

Citations:

Zbl 1062.94033
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