论文信息 - Cyclotomy and Addition Sets

Cyclotomy and Addition Sets

Abstract In this paper, we develop methods to solve the polynomial congruence θ(x)θ(xg) ≡ d + λ(1 + x +… + xp−1) (mod xp − 1), where p is an odd prime and θ(x) is a polynomial with nonnegative integral coefficients. Using these methods, we construct some new addition sets that are the unions of index classes for some primes p. We also establish the nonexistence of both the (95, 10, 1, 18)-addition set and the (95, 10, 1, 56)-addition set.

Clement W. H. Lam

[1] C. Lam,et al. On rational circulants satisfying A2=dI+λJ☆ , 1975 .

[2] L. D. Baumert. Cyclic Difference Sets , 1971 .

[3] Leonard Eugene Dickson,et al. Cyclotomy, Higher Congruences, and Waring's Problem II , 1935 .

[4] Albert Leon Whiteman,et al. The cyclotomic numbers of order twenty , 1960 .

[5] T. Storer. Cyclotomy and difference sets , 1967 .

[6] Emma Lehmer. On the number of solutions ofuk+D≡w2(modp) , 1955 .

[7] Clement W. H. Lam. A Generalization of Cyclic Difference Sets II , 1975, J. Comb. Theory, Ser. A.

[8] Emma Lehmer. On the number of solutions of $u^k+D\equiv w^2(\mod p)$. , 1955 .

[9] Emma Lehmer. On the number of solutions of uk + D ≡ w2( mod p) , 1955 .

[10] Marshall Hall,et al. A survey of difference sets , 1956 .

[11] Clement W. H. Lam. Nth Power Residue Addition Sets , 1976, J. Comb. Theory, Ser. A.