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1-perfect codes over self-complementary graphs

Commentationes Mathematicae Universitatis Carolinae

A Characterization of Designs Related to the Witt System S(5, 8, 24).

Mathematische Zeitschrift

A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications

Serdica Journal of Computing

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

Serdica Journal of Computing

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  and Maruta ,  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 $n$-quasigroups of order 4.

Sibirskij Matematicheskij Zhurnal

Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths

Serdica Journal of Computing

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.

The Electronic Journal of Combinatorics [electronic only]

Codes that attain minimum distance in every possible direction

Open Mathematics

The following problem motivated by investigation of databases is studied. Let $𝒞$ be a q-ary code of length n with the properties that $𝒞$ 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.

The Electronic Journal of Combinatorics [electronic only]

Évariste Galois et la planète Mars : introduction à la théorie algébrique du codage

Publications mathématiques et informatique de Rennes

Extremal Polynomials for Obtaining Bounds for Spherical Codes and Designs.

Discrete &amp; computational geometry

Gray codes for $A$-free strings.

The Electronic Journal of Combinatorics [electronic only]

Information sets as permutation cycles for quadratic residue codes.

International Journal of Mathematics and Mathematical Sciences

Intersections of $q$-ary perfect codes.

Sibirskij Matematicheskij Zhurnal

Lattice-Like Total Perfect Codes

Discussiones Mathematicae Graph Theory

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

Publications de l'Institut Mathématique

O jednom problému z theorie kodování

Časopis pro pěstování matematiky

On perfect-like binary and non-binary linear codes - a brief survey.

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

On the failing cases of the Johnson bound for error-correcting codes.

The Electronic Journal of Combinatorics [electronic only]

Perfect codes and two-graphs

Commentationes Mathematicae Universitatis Carolinae

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