Almost weakly self-dual bases for finite fields

We characterize almost weakly self-dual polynomial bases for the finite field over , where denotes the finite field of order q a prime power. We also extend a formula for the excess of certain polynomial bases from the case q = 2 to general q.

[1]  Miodrag Živković Table of primitive binary polynomials. II , 1994 .

[2]  Douglas R. Stinson On bit-serial multiplication and dual bases in GF(2m) , 1991, IEEE Trans. Inf. Theory.

[3]  Scott A. Vanstone,et al.  On the Number of Self-Dual Bases of GF(q m ) Over GF(q) , 1990 .

[4]  Dieter Gollmann,et al.  Self-dual bases in $$\mathbb{F}_{q^n } $$ , 1993, Des. Codes Cryptogr..

[5]  S. Vanstone,et al.  On primitive polynomials over finite fields , 1989 .

[6]  Stephen D. Cohen,et al.  UNIFORM DISTRIBUTION OF POLYNOMIALS OVER FINITE FIELDS , 1972 .

[7]  Aimo Tietäväinen Proof of a conjecture of S. Chowla , 1975 .

[8]  G. Mullen,et al.  Primitive polynomials over finite fields , 1992 .

[9]  R. Ree,et al.  Proof of a conjecture of S. Chowla , 1971 .

[10]  Gérald E. Séguin,et al.  Low complexity normal bases for F2mn , 1990, Discret. Appl. Math..

[11]  Stephen D. Cohen,et al.  Primitive elements and polynomials with arbitrary trace , 1990, Discret. Math..

[12]  Willi Geiselmann,et al.  Weakly self-dual normal bases in finite fields , 1996 .

[13]  A. Menezes,et al.  Applications of Finite Fields , 1992 .

[14]  S. D. Cohen COMPUTATIONAL AND ALGORITHMIC PROBLEMS IN FINITE FIELDS , 1994 .

[15]  Stephen D. Cohen The distribution of polynomials over finite fields, II , 1972 .

[16]  Dieter Jungnickel,et al.  Trace-Orthogonal Normal Bases , 1993, Discret. Appl. Math..

[17]  Gary L. Mullen Bases and the distribution of irreducible and primitive polynomials over finite fields , 1996 .

[18]  Stephen D. Cohen,et al.  The distribution of polynomials over finite fields , 1970 .

[19]  Miodrag Živković A table of primitive binary polynomials , 1994 .

[20]  Shuhong Gao,et al.  Optimal normal bases , 1992, Des. Codes Cryptogr..

[21]  Ronald C. Mullin,et al.  Optimal normal bases in GF(pn) , 1989, Discret. Appl. Math..