1-perfect codes over self-complementary graphs
A Characterization of Designs Related to the Witt System S(5, 8, 24).
A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications
ACM Computing Classification System (1998): E.4.Let q be a prime or a prime power ≥ 3. The purpose of this paper is to give a necessary and sufficient condition for the existence of an (n, r)-arc in PG(2, q ) for given integers n, r and q using the geometric structure of points and lines in PG(2, q ) for n > r ≥ 3. Using the geometric method and a computer, it is shown that there exists no (34, 3) arc in PG(2, 17), equivalently, there exists no [34, 3, 31] 17 code.This research was partially...
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...
Asymptotics for the number of -quasigroups of order 4.
Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths
Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant...
Codes, lattices, and Steiner systems.
Codes that attain minimum distance in every possible direction
The following problem motivated by investigation of databases is studied. Let be a q-ary code of length n with the properties that has minimum distance at least n − k + 1, and for any set of k − 1 coordinates there exist two codewords that agree exactly there. Let f(q, k)be the maximum n for which such a code exists. f(q, k)is bounded by linear functions of k and q, and the exact values for special k and qare determined.
Covering codes for Hats-on-a-line.
Évariste Galois et la planète Mars : introduction à la théorie algébrique du codage
Extremal Polynomials for Obtaining Bounds for Spherical Codes and Designs.
Gray codes for -free strings.
Information sets as permutation cycles for quadratic residue codes.
Intersections of -ary perfect codes.
Lattice-Like Total Perfect Codes
A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λn via pairs (G, Φ) formed by abelian groups G and homomorphisms Φ: Zn → G. A conjecture is posed that the cited contribution covers all possible cases. A related conjecture on the unfinished work on open problems on lattice-like perfect dominating sets in Λn with induced components that are parallel paths of length > 1 is posed as well.
Note on Gray Codes for Permutation Lists
O jednom problému z theorie kodování
On perfect-like binary and non-binary linear codes - a brief survey.
On the failing cases of the Johnson bound for error-correcting codes.
Perfect codes and two-graphs