منابع مشابه
On the Reed-Muller codes
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 eld. We also establish the existence of two short exact sequences that lead to new proofs that the minimum-we...
متن کاملNotes on Reed-Muller Codes
In this paper, we consider the Reed-Muller (RM) codes. For the 1st order RM code, we prove that it is unique in the sense that any linear code with the same length, dimension and minimum distance must be the 1st order RM code; For the 2nd order RM code, we give a constructive linear sub-code family for the case when m is even. This is an extension of Corollary 17 of Ch. 15 in the book by MacWil...
متن کاملQuantum 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.
متن کاملGeneralized 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...
متن کاملQuantum 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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90526-l