The Dual Code of some Reed-Muller type Codes
✍ Scribed by M. González-Sarabia; C. Rentería
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 108 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0938-1279
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
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
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
Let R(r, m) be the rth order Reed-Muller code of length 2 '~, and let p(r, m) be its covering radius. We prove that if 2 \_< k -< m -r -1, then p(r + k, m + k) > #(r, m) + 2(k -1). We also prove that if m -r > 4, 2 < k < m -r -1, and R(r, m) has a coset with minimal weight pfr, m) which does not co
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