Topic
MAXEkSAT
About: MAXEkSAT is a research topic. Over the lifetime, 147 publications have been published within this topic receiving 5947 citations.
Papers published on a yearly basis
Papers
TL;DR: It is shown in this paper that the iterative algorithm introduced by Berlekamp for decoding BCH codes actually provides a general solution to the problem of synthesizing the shortest linear feedback shift register capable of generating a prescribed finite sequence of digits.
Abstract: It is shown in this paper that the iterative algorithm introduced by Berlekamp for decoding BCH codes actually provides a general solution to the problem of synthesizing the shortest linear feedback shift register capable of generating a prescribed finite sequence of digits. The shift-register approach leads to a simple proof of the validity of the algorithm as well as providing additional insight into its properties. The equivalence of the decoding problem for BCH codes to a shift-register synthesis problem is demonstrated, and other applications for the algorithm are suggested.
2,462 citations
TL;DR: A general method of constructing error correcting binary group codes is obtained and an example is worked out to illustrate the method of construction.
Abstract: A general method of constructing error correcting binary group codes is obtained. A binary group code with n places, k of which are information places is called an (n,k) code. An explicit method of constructing t-error correcting (n,k) codes is given for n = 2m−1 and k = 2m−1−R(m,t) ≧ 2m−1−mt where R(m,t) is a function of m and t which cannot exceed mt. An example is worked out to illustrate the method of construction.
1,457 citations
TL;DR: In this article, it was shown that a BCH code of length n can contain its dual code only if its designed distance delta = O(radicn), and the converse was proved in the case of narrow-sense codes.
Abstract: Classical Bose-Chaudhuri-Hocquenghem (BCH) codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its dual code only if its designed distance delta=O(radicn), and the converse is proved in the case of narrow-sense codes. Furthermore, the dimension of narrow-sense BCH codes with small design distance is completely determined, and - consequently - the bounds on their minimum distance are improved. These results make it possible to determine the parameters of quantum BCH codes in terms of their design parameters
419 citations
TL;DR: It is shown that a classical error correcting code C, which contains its dual, C/sup /spl perp///spl sube/C, and which can be enlarged to C'=[n,k'>k+1,d'], can be converted into a quantum code of parameters [[ n,k+k'-n,min(d,[3d'/2])]].
Abstract: It is shown that a classical error correcting code C=[n,k,d] which contains its dual, C/sup /spl perp///spl sube/C, and which can be enlarged to C'=[n,k'>k+1,d'], can be converted into a quantum code of parameters [[n,k+k'-n,min(d,[3d'/2])]] This is a generalization of a previous construction, it enables many new codes of good efficiency to be discovered Examples based on classical Bose-Chaudhuri-Hocquenghem (BCH) codes are discussed
318 citations
TL;DR: The decoding of BCH codes readily reduces to the solution of a certain key equation and an iterative algorithm is presented for solving this equation over any field.
Abstract: The decoding of BCH codes readily reduces to the solution of a certain key equation. An iterative algorithm is presented for solving this equation over any field. Following a heuristic derivation of the algorithm, a complete statement of the algorithm and proofs of its principal properties are given. The relationship of this algorithm to the classical matrix methods and the simplification which the algorithm takes in the special case of binary codes is then discussed. The generalization of the algorithm to BCH codes with a slightly different definition, the generalization of the algorithm to decode erasures as well as errors, and the extension of the algorithm to decode more than t errors in certain eases are also presented.
121 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 2 |
| 2016 | 9 |
| 2015 | 3 |
| 2014 | 11 |
| 2013 | 8 |
| 2012 | 7 |