Abstract
The shortest possible length of a q-ary linear code of covering radius R and codimension r is called the length function and is denoted by ℓ q (r, R). Constructions of codes with covering radius 3 are here developed, which improve best known upper bounds on ℓ q (r, 3). General constructions are given and upper bounds on ℓ q (r, 3) for q = 3, 4, 5, 7 and r ≤ 24 are tabulated.
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Communicated by Pascale Charpin.
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Davydov, A.A., Östergård, P.R.J. Linear codes with covering radius 3. Des. Codes Cryptogr. 54, 253–271 (2010). https://doi.org/10.1007/s10623-009-9322-y
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DOI: https://doi.org/10.1007/s10623-009-9322-y