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**publisher and metadata sources**).Minimal saturating sets in projective spaces PG(n, q) are considered. Estimates and exact values of some extremal parameters are given. In particular the greatest cardinality of a minimal… Continue Reading

For a prime power q and for integers R, η with R > 0, 0 ≤ η ≤ R − 1, let A R,q = (Cni)i denote an infinite sequence of q-ary linear [ni, ni − ri]qR codes Cni with covering radius R and such that the… Continue Reading

A concept of locally optimal (LO) linear covering codes is introduced in accordance with the concept of minimal saturating sets in projective spaces over finite fields. An LO code is nonshortening in… Continue Reading

Infinite families of linear codes with covering radius R=2, 3 and codimension tR+1 are constructed on the base of starting codes with codimension 3 and 4. Parity-check matrices of the starting codes… Continue Reading

XV International Symposium Problems of Redundancy…

In a projective plane Π<sub>q</sub> (not necessarily Desar-guesian) of order q, a point subset S is saturating (or dense) if any point of Π<sub>q</sub>\S is collinear with two points in S. Using… Continue Reading

Abstract We show that no additive [ 15 , 5 , 9 ] 4 -code exists. As a consequence the largest dimension k such that an additive quaternary [ 15 , k , 9 ] 4 -code exists is k = 4.5 .

The non-existence of $$[29+h,3+h,26]_{16}$$[29+h,3+h,26]16 and $$[29+h,4+h,25]_{16}$$[29+h,4+h,25]16-codes, $$h\ge 0$$h≥0, is proven. These results are obtained using geometrical methods, exploiting… Continue Reading