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On the Reed-Muller codes

✍ Scribed by E.F. Assmus Jr

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
632 KB
Volume
106-107
Category
Article
ISSN
0012-365X

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✦ Synopsis

Assmus Jr, E.F., On the Reed-Muller codes, Discrete Mathematics 106/107 (1992) 25-33.

We give a brief but complete account of all the essential facts concerning the Reed-Muller and punctured

Reed-Muller codes. The treatment is new and includes an easy, direct proof of the fact that the punctured Reed-Muller codes are the codes of the projective geometries over the binary field. We also establish the existence of two short exact sequences that lead to new proofs that the minimum-weight vectors of the Reed-Muller and punctured Reed-Muller codes are the incidence vectors of the appropriate geometric objects.

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