Códigos de Reed-Muller

Codes de Reed-Muller et cryptanalyse du registre filtré

Quantum Reed-Muller Codes

This paper presents a set of quantum Reed-Muller codes which are typically 100 times more effective than existing quantum Reed-Muller codes. The code parameters are [[n, k, d]] = [[2, ∑r l=0 C(m, l) − ∑m−r−1 l=0 C(m, l), 2 m−r ]] where 2r + 1 > m > r.

Generalized Reed-Muller Codes

the possible choices for n and k are rather thinly distributed in the class of all pairs (n, k) with k ~ n--and it is, therefore, often inefficient to make use of such codes in concrete situations (that is, when a desired pair (n, k) is far from any achievable pair). We have succeeded in overcoming this difficulty by generalizing the Reed-Muller codes in such a way that they exist for every pai...

Quantum Reed-Muller codes

A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n, k, d]] = [[2r, 2r −C(r, t)− 2 ∑t−1 i=0 C(r, i), 2 t + 2t−1]]. The study of quantum information is currently stimulating much interest. Most of the basic concepts of classical information theory have counterparts in quantum information theory, and among these is the idea of a...

Projective Reed - Muller Codes

R~sum~. On inlroduit une classe de codes lintaires de la famille des codes de Reed-Muller, les codes de Reed-Muller projectifs. Ces codes sont des extensions des codes de Reed-Muller gtntralists ; les codes de Reed-Muller projectifs d'ordre I atteignent la borne de Plotkin. On donne les traram&res des codes de Reed-Muller projecfifs d'ordre 2. 1.Introduction We note pm(Fq) the projective space ...