Linear codes over finite chain rings.
On Blocking Sets in Affine Hjelmslev Planes
ACM Computing Classification System (1998): G.2.1. We prove that the minimum size of an affine blocking set in the affine plane AHG ... This research has been supported by the Scientific Research Fund of Sofia University under Contract No 109/09.05.2012.
New Symmetric (61,16,4) Designs Invariant Under the Dihedral Group of Order 10
∗ This work has been partially supported by the Bulgarian NSF under Contract No. I-506/1995. In this note we construct five new symmetric 2-(61,16,4) designs invariant under the dihedral group of order 10. As a by-product we obtain 25 new residual 2-(45,12,4) designs. The automorphism groups of all new designs are computed.
On Multiple Deletion Codes
In 1965 Levenshtein introduced the deletion correcting codes and found an asymptotically optimal family of 1-deletion correcting codes. During the years there has been a little or no research on t-deletion correcting codes for larger values of t. In this paper, we consider the problem of finding the maximal cardinality L2(n;t) of a binary t-deletion correcting code of length n. We construct an infinite family of binary t-deletion correcting codes. By computer search, we construct t-deletion codes...
The Nonexistence of some Griesmer Arcs in PG(4, 5)
In this paper, we prove the nonexistence of arcs with parameters (232, 48) and (233, 48) in PG(4,5). This rules out the existence of linear codes with parameters [232,5,184] and [233,5,185] over the field with five elements and improves two instances in the recent tables by Maruta, Shinohara and Kikui of optimal codes of dimension 5 over F5.
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