摘要: Let K ⊂ L be a finite Galois extension of fields, degree n. G the group, and let (<α)<∈G normal basis for over K. An argument due to Mullin, Onyszchuk, Vanstone Wilson (Discrete Appl. Math. 22 (1988/89), 149–161) shows that matrix describes map x → αx on this has at least 2n - 1 nonzero entries. If it contains exactly entries, then is said optimal. In present paper we determine all optimal bases. case our result confirms conjecture was made by Mullin et al. computer search.
springer.com
sci-hub.se 参考文章(2)
R.C. Mullin, I.M. Onyszchuk, S.A. Vanstone, R.M. Wilson, Optimal normal bases in GF( p n ) Discrete Applied Mathematics. ,vol. 22, pp. 149- 161 ,(1989) , 10.1016/0166-218X(88)90090-X
R. C. Mullin, A characterization of the extremal distributions of optimal normal bases Proceedings of the Marshall Hall conference on Coding theory, design theory, group theory. pp. 41- 49 ,(1993)