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A note on the covering radius of optimum codes

✍ Scribed by M.C. Bhandari; M.S. Garg

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
514 KB
Volume
33
Category
Article
ISSN
0166-218X

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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

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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 BC