Explicit sequence expansions.

*(English)*Zbl 1005.11064
Ding, C. (ed.) et al., Sequences and their applications. Proceedings of the international conference, SETA ’98, Singapore, December 14-17, 1998. London: Springer. Springer Series in Discrete Mathematics and Theoretical Computer Science. 308-317 (1999).

Summary: Examples of \(d\)-perfect sequences are constructed based on the method in [C. Xing and K. Y. Lam, IEEE Trans. Inf. Theory 45, 1267-1270 (1999; Zbl 0943.94008); C. Xing, H. Niederreiter, K. Y. Lam and C. Ding, Finite Fields Appl. 5, 301-313 (1999; Zbl 0943.94005)]. In particular examples of 1-perfect sequences based on genus 0 curves over binary and the ternary fields are computed, as are 2-perfect binary sequences based on an elliptic curve. The complexity profile of certain of the 2-perfect sequences are experimentally determined to follow that of 1-perfect sequences. Based on two algebraic reformulations of the known characterization of binary 1-perfect sequences, these sequences are proved to be 1-perfect.

For the entire collection see [Zbl 0974.00035].

For the entire collection see [Zbl 0974.00035].

##### MSC:

11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |

94A55 | Shift register sequences and sequences over finite alphabets in information and communication theory |