Showing papers in "Finite Fields and Their Applications in 2004"

TL;DR: There are today no sporadic examples of difference sets with Singer parameters; i.e. every known such difference set belongs to a series given by a constructive theorem.

TL;DR: If F is finite then the polynomial f has exactly n rational roots, and it is found the exact number of a[email protected]?F^x such that f has n rational Roots, for each n.

TL;DR: Using the Teichmuller character and Gauss sums, the following results are obtained concerning p-ary bent functions and q-ary resilient functions: a characterization of certain q-ARY resilient functions in terms of their coefficients.

TL;DR: It is shown that the dual code of the binary cyclic code of length 2^m-1 with two zeros @a,@a^d cannot have three weights in the case that m is even and d=0(mod3).

TL;DR: In this paper, the primitive idempotents in the ring R"p"^"n=GF(q)[x]/(x^p^^^n-1), for any positive integer n, are obtained in terms of cyclotomic numbers, provided p does not divide @l if n>=2.

TL;DR: It is shown that any left MacWilliams basic ring is Frobenius, and a strategy is proposed that would reduce the question to problems dealing only with matrices over finite fields.

TL;DR: It is shown that optical orthogonal codes with auto- and cross-correlations at most 2 can be obtained from conics on a finite projective plane and the obtained codes asymptotically attain the upper bound on the number of codewords when the order q of the base field is large enough.

TL;DR: All the diversities for [n,k,d]"q codes with k>=3, [email protected]?-2(modq) are found and characterized with their spectra geometrically, which yields that such codes are extendable for all odd q>=5.

TL;DR: Improvements are made on the genus of subfields of the Hermitian function field which are the fixed subfield of subgroups of the automorphism group.

TL;DR: For a prime power q=p^s, some recurrent methods for constructing families of monic irreducible polynomials of degree np^k,k>=1, over F"q is given.

TL;DR: The weights of two-dimensional (2-D) cyclic codes are studied and a relation between the weights of codewords and a family of Artin-Schreier curves is found, which gives a lower bound on the minimum distance.

TL;DR: In this article, it was shown that there exists a primitive polynomial f(x)=x n-a"1x^n^-^1++(-1)^na"n over F"q of degree n with the first three coefficients a"1,a"2,a"3 prescribed when n>=8.

TL;DR: The number of sequences @h of length n with given largest dimension S"n(@h)=S for passing this lattice test is determined and an exact formula for the expected value is derived.

TL;DR: It is shown that X is F"q"^"2-isomorphic to the nonsingular model of a curve given by P(y)=A(x) under the further hypothesis that a certain field extension is Galois.

TL;DR: The characteristic polynomials of the Frobenius endomorphism on the etale @?-adic cohomology groups of the curve are given, giving a formula for the number of rational points of projective algebraic curves defined over a finite field, and a bound ''a la Weil'' for connected ones.

TL;DR: A new construction of digital nets, and more generally of (d,k,m,s)-systems, over finite fields which is an analog of the matrix-product construction of codes is presented.

TL;DR: In this paper, the density of elements in F p ∗ having order, respectively index, congruent to a ( mod d) is determined, where the average is taken over all finite fields of prime order.

TL;DR: The exact shape of the G"2 equidistribution law for the one parameter family of exponential sums over F"p^x,@?xmodp,x 0@g"2(x)exp(2@pi(x^7+tx)/p) is determined.

TL;DR: This paper considers rational models representing all k-isomorphy classes of curves with a given arithmetic structure for the ramification divisor and finds necessary and sufficient conditions for two models of the same type to be k- isomorphic.

TL;DR: For any q which is a power of 2, a finite subgroup of GL"q(C) under which the complete weight enumerators of generalized doubly-even self-dual codes over F"q are invariant is described.

TL;DR: This paper deals with the remaining cases and proves that there exists a primitive polynomial of degree 7 over F"q with the first three coefficient prescribed where the characteristic of F" q is 2 or 3.

TL;DR: This paper constructs a projective system X defined as a set of n-linear subspaces on the dual projective space of a poset code that gives a natural one-to-one correspondence between the set of equivalence classes of nondegenerate poset projective systems and theSet of nondEGenerate Poset codes.

TL;DR: This paper improves [email protected]?nyi's embeddability result on (k,p)-arcs, in PG(2,q), q=p^h, p prime, and proved that for k>[email protected], @e= q+1-q, any k-arc can be extended to a hyperoval.

TL;DR: Boneh and Venkatesan as discussed by the authors showed that a reasonably small portion of most significant bits of the Diffie-Hellman key modulo a prime are as secure as the whole key.

TL;DR: It is proved that if two normal elements have the same multiplication table, then they are conjugates and the partial converse to the known fact that if @a generates a Type I optimal normal basis in F"2"^"n, then its dual basis has complexity 3n-3.

TL;DR: It is shown that the normalized character of the associated permutation representation of S"n approaches the trivial character as n approaches infinity, and a conjecture is formed that would yield the asymptotic number of distinct equivalence classes of q-ary linear codes.

TL;DR: If u is uniformly distributed modp^S, then it is Uniformly distributed mod p^s for all s>=1, which solves a longstanding folklore conjecture.

TL;DR: It is proved that a class of q-ary dual BCH-codes in characteristic 2 produce caps in AG(4,q), and the weight distribution of the codes generated by the caps is determined via a close link to the binary Kloosterman codes, the dual Melas codes.

TL;DR: It is proved that a matrix of minimum q-rank is unique up to a monomial equivalence, and the related symmetric net is a classical net in the n-dimensional affine geometry AG(n,q).

TL;DR: The number and representatives of isomorphism classes of hyperelliptic curves of genus g defined over finite fields F"("2"g"+"1")"^"n, g=1,2,3,3" are given.