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On the covering radius of cyclic linear codes and arithmetic codes

✍ Scribed by Tor Helleseth

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
781 KB
Volume
11
Category
Article
ISSN
0166-218X

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✦ Synopsis

The problem of finding the covering radius and minimum distance of algebraic and arithmetic codes is shown to be related to Waring's problem i n a finite field and to the theory of cyclotomic numbers. The methods devel oped l ead to new results for the covering radius of certain f-errorcorrecting BCH codes. Further, new results are given for the covering radius and the minimum distance of some classes of arithmetic codes generated by prime numbers.

πŸ“œ SIMILAR VOLUMES

On the covering radius of Reed-Muller co
On the covering radius of Reed-Muller codes
✍ GΓ©rard D. Cohen; Simon N. Litsyn πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 371 KB

We present lower and upper bounds on the covering radius of Reed-Muller codes, yielding asymptotical improvements on known results. The lower bound is simply the sphere covering one (not very new). The upper bound is derived from a thorough use of a lemma, the 'essence of Reed-Mullerity'. The idea