In Section 8, upper bounds on the length function ℓ q ( t R + 1 , R ) are obtained for growing t ≥ 1 . These bounds are provided by infinite families of ...

Aug 31, 2021 · Upper bounds on the length function for covering codes with covering radius R and codimension tR+1. In the literature, for q=(q')^R with q' a ...

Nov 29, 2021 · In this work, new upper bounds on `q(tR + 1,R) are obtained in the following forms: (a) `q(r, R) ≤ cq(r−R)/R · R p lnq, R ≥ 3, r = tR + 1, t ...

The bounds of this paper are better than the known ones; however, when the author's paper is an arbitrary prime power, the bounds of the paper are worse ...

If covering radius and codimension are fixed then the covering problem for codes is that of finding codes with small length and/or obtaining good upper bounds ...

Oct 22, 2024 · The smallest possible length of a $q$-ary linear code of covering radius $R$ and codimension (redundancy) $r$ is called the length function and ...

In this work, new upper bounds on ℓ_q(tR+1,R) are obtained in the following forms: (a) ℓ_q(r,R)≤ cq^(r-R)/R·√(ln q), R≥3, r=tR+1, t≥1, (a) q is an arbitrary ...

We improve this upper bound significantly by showing con- structively that d is bounded from above by the cardinality of any binary covering code with length n ...

Improved upper bounds are presented for K(n, r), the minimum cardinality of a binary code of length n and covering radius r. The new bounds are obtained by ...

This paper is devoted to the upper bound on the length function ℓ q ( 3 t + 1 , 3 ) , t ≥ 1 . Let P ...