Linear codes with covering radius 3 |
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| Authors: | Alexander A Davydov Patric R J Östergård |
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| Institution: | 1.Institute for Information Transmission Problems, Russian Academy of Sciences,Moscow,Russian Federation;2.Department of Communications and Networking,Helsinki University of Technology TKK,TKK,Finland |
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| 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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| Keywords: | |
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