✦ LIBER ✦

The automorphism group of Generalized Reed-Muller codes

✍ Scribed by Thierry Berger; Pascale Charpin

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 1008 KB
Volume: 117
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90321-j

No coin nor oath required. For personal study only.

✦ Synopsis

Berger, T. and P. Charpin, The automorphism group of Generalized Reed-Muller codes, Discrete Mathematics 117 (1993) l-17.

We prove that the automorphism group of Generalized Reed-Muller codes is the general linear nonhomogeneous group. The Generalized Reed-Muller codes are introduced by Kasami, Lin and Peterson. An extensive study was made by Delsarte, Goethals and Mac-Williams; our result follows their description of the minimum weight codewords. An automorphism of a cyclic q-ary code is here a substitution over the field GF(q"). In the more general case where the automorphisms are defined by monomial matrices, we also obtain the automorphism group (called the monomial group) as the direct product of the general linear nonhomogeneous group with the multiplicative group of the alphabet field.

📜 SIMILAR VOLUMES

On the Reed-Muller codes

✍ E.F. Assmus Jr 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 632 KB

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 R

Generalized Reed–Muller Codes and Curves

Generalized Reed–Muller Codes and Curves with Many Points

✍ G van der Geer; M van der Vlugt 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 236 KB

Words of low weight in trace codes correspond to curves with many points and the same holds for subcodes of low weight via the fibre product construction. In 1996 Heijnen and Pellikaan gave an algorithm to determine a basis of minimum weight subcodes of generalized Reed Muller codes. We show how thi

Divisors of codes of Reed-Muller type

✍ Harold N. Ward 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 856 KB

On the covering radius of Reed-Muller co

On the covering radius of Reed-Muller codes

✍ Gérard D. Cohen; Simon N. Litsyn 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 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

Incidence codes of posets: Eulerian pose

Incidence codes of posets: Eulerian posets and Reed-Muller codes

✍ Kenneth P. Bogart 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 713 KB

This paper shows how to construct analogs of Reed-Muller codes from partially ordered sets. In the case that the partial:; ordered set is Eulertan the length of the code is the number of elements in the poset, the dimension is the size of a sePected order ideal and the minimum distance is the minimu

Reed-Muller-Type Codes Over the Segre Va

Reed-Muller-Type Codes Over the Segre Variety

✍ M. González-Sarabia; C. Renterı́a; H. Tapia-Recillas 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 124 KB

The a-invariant is determined and a description of the defining ideal for the set S K of rational points of the Segre variety over a finite field K is given. The dimension as well as the minimum distance of a Reed-Muller-type linear code defined over S K are also determined. An example is given to i