Orphan structure of the first-order Reed-Muller codes
نویسندگان
چکیده
منابع مشابه
Orphan structure of the first-order Reed-Muller codes
Brualdi, R.A., N. Cai and VS. Pless, Orphan structure of the first-order Reed-Muller codes, Discrete Mathematics 102 (1991) 239-247. We investigate a method of combining two codes which we call the outer product. First-order Reed-Muller codes are outer products of a number of copies of the full binary space of length 2, and we apply our results to obtain cosets of the Reed-Muller codes which ha...
متن کاملPartial permutation decoding for the first-order Reed-Muller codes
Partial permutation decoding is shown to apply to the first-order Reed–Muller codes R(1,m), where m > 4 by finding s-PD-sets for these codes for 2 ≤ s ≤ 4. © 2008 Elsevier B.V. All rights reserved.
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90118-y