New nonbinary sequence families with low correlation, large size, and large linear span

✍ Scribed by Zhengchun Zhou; Xiaohu Tang

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 225 KB
• Volume: 24
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2011.01.033

✦ Synopsis

Let p be an odd prime and n = (2m + 1)e. Based on the theory of quadratic forms over finite fields of odd characteristic, we generalize the binary construction by Yu and Gong to p-ary case. As a result, we obtain a new family F k o (ρ) of p-ary sequences of period p n -1 for arbitrary positive integers 1 ≤ ρ ≤ m and k with gcd(n, k) = e. It is shown that, for a given ρ, F k o (ρ) has family size p nρ , maximum correlation 1 + p n+(2ρ-1)e 2

, and maximum linear span (m + 1)n. In particular, the new family F k o (ρ) contains Tang, Udaya, and Fan's construction as a subset, if an m-sequence is excluded.