Comments on "On the covering radius of codes" [with reply]
β Scribed by Bhandari, M.C.; Garg, M.S.; Graham, R.L.; Sloane, N.J.A.
- Book ID
- 114540520
- Publisher
- IEEE
- Year
- 1990
- Tongue
- English
- Weight
- 185 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0018-9448
- DOI
- 10.1109/18.53766
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π SIMILAR VOLUMES
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
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