Algorithme de Brill-Noether et codes de Goppa
Alon-Babai-Suzuki's conjecture related to binary codes in nonmodular version.
An asymptotic Gilbert-Varshamov bound for -nets.
An extremal doubly even self-dual code of length 112.
An Improvement to the Achievement of the Griesmer Bound
We denoted by nq(k, d), the smallest value of n for which an [n, k, d]q code exists for given q, k, d. Since nq(k, d) = gq(k, d) for all d ≥ dk + 1 for q ≥ k ≥ 3, it is a natural question whether the Griesmer bound is attained or not for d = dk , where gq(k, d) = ∑[d/q^i], i=0,...,k-1, dk = (k − 2)q^(k−1) − (k − 1)q^(k−2). It was shown by Dodunekov [2] and Maruta [9], [10] that there is no [gq(k, dk ), k, dk ]q code for q ≥ k, k = 3, 4, 5 and for q ≥ 2k − 3, k ≥ 6. The purpose of this paper...
Applications entrée-sortie sur un corps fini
Applications of the ‘Ham Sandwich Theorem’ to Eigenvalues of the Laplacian
We apply Gromov’s ham sandwich method to get: (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in Euclidean space.
Association schemes and MacWilliams dualities for generalized Niederreiter-Rosenbloom-Tsfasman posets [Book]
Asymptotics for the number of -quasigroups of order 4.
Automorphism groups of Ree type Deligne-Lusztig curves and function fields.
Balanced Gray codes.
Balancing cyclic -ary Gray codes.
Balancing cyclic -ary Gray codes. II.
Bezpečnostní kódy v železničních zabezpečovacích zařízeních
Binary codes and partial permutation decoding sets from the odd graphs
For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ωk, the set of all k-subsets of Ω = 1, 2, …, 2k +1, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = /0. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k 4 is determined. Lastly, the relationship between the dual code from O(k)...
Bounds for digital nets and sequences
Bounds for DNA codes with constant GC-content.
Calculation of the detection properties in the binary symmetrical channel
One of the important parts of railway signalling systems design is the safety of communication, achievable - among others - with the error detecting code. Getting evidence of quantitative safety targets, especially the probability of undetected error of the code, is a surprisingly complicated issue. We've analysed 2048 irreducible self-adjoint generator polynomials of the degree 32. More than 70 of these have a maximum probability of failure lower than the standard codes generally used. In this...
Characterisation of Some Steiner Systems, Parallelisms, and Biplanes.
Charakterisierung redundanzfreier codes zur datenverschlüsselung