New Family of $p$ -ary Sequences With Optimal Correlation Property and Large Linear Span
Ji-Woong Jang, Young Sik Kim, Jong‐Seon No, Tor Helleseth · IEEE Transactions on Information Theory · 2004
For an odd prime p and integers n, m, and k such that n=(2m+1)k, a new family of p-ary sequences of period p/sup n/-1 with optimal correlation property is constructed using the p-ary Helleseth-Gong sequences with ideal autocorrelation, where the size of the sequence family is p/sup n/. That is, the maximum nontrivial correlation value R/sub max/ of all pairs of distinct sequences in the family does not exceed p/sup n/2/+1, which means the family has optimal correlation in terms of Welch's lower bound. The symbol distribution of the sequences in the family is enumerated. It is also shown that the linear span of the sequences in the family is (m+2)n except for the m-sequence in the family.