Minimum distance of cyclic codes
On additive cyclic codes
... the minimum distance of cyclic codes which is obtained by relating the weights of codewords and the number of rational points on certain algebraic curves (see ...of cyclic codes ...
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A Note on the Rank Bounded Distance and Its Algorithms for Cyclic Codes
... The minimum distance for linear codes is one of the important ...the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa ...
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CONSTRUCTION OF REGULAR QUASI CYCLIC-LOW DENSITY PARITY CHECK CODES FROM CYCLIC CODES
... derived cyclic code; we have reduced in half the incidence vectors of matrix H LDPC and have improved the error-correcting performance of QC-LDPC ...LDPC codes have high density, high rates and the ...
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Quantum Codes from Cyclic Codes over GF (4 m )
... self-orthogonal codes over GF (4) that are obtained as 4-ary images of 4 m -ary cyclic codes of length n |(4 m − ...self-orthogonal codes over GF (2 m ) have been used to obtain quantum ...
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List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes
... Product codes, we computed its error bound and ...Reed-Solomon codes as constituent codes, the algorithm does not become computationally ...Reed-Solomon codes is the possibility of con- ...
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Families of Cyclic Codes over Finite Chain Rings
... Theorem 18. Let n be a prime of the form n ≡ 3 (mod 4), and let (q, n) = 1. If q is a quadratic residue modulo n, then there exists a pure [[n, 1, d]] R stabilizer code with distance d satisfying d 2 − d + 1 ≥ n. ...
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A New Powerful Scheme Based on Self Invertible Stabilizer Multiplier Permutation to Find the Minimum Distance for large BCH Codes
... correcting codes improve the reliability of such communication, notably on channels that are subject to noise, by adding redundancy in ...BCH codes are a family of cyclic codes, which are used ...
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Cyclic Orbit Codes with the Normalizer of a Singer Subgroup
... orbit codes of a Singer subgroup are not large but taking the unions of them is a nice idea to obtain large cyclic subspace codes for a given minimum ...
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A parallel Viterbi decoder for block cyclic and convolution codes
... Hamming distance of the codeword that is legitimately generated via state R for the ith input bit, from the actual input ...Hamming distance less than or equal to the minimum code separation, d min ...
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A Low Complexity Detection Scheme of Space Frequency Codes for MIMO OFDM Systems with Minimum Euclidean Distance Metric Calculation
... Then this is fed into IFFT block.The output is converted back into the serial signal and fed into the antenna for transmission.Figure 2 depicts this. Figure 3 shows the receiver section of MIMO OFDM systems.The signals ...
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Chapter 1. Search for Good Linear Codes in the Class of Quasi-Cyclic and Related Codes
... to minimum distance, Vardy showed that finding the minimum distance of a linear code over a fixed finite field is ...the minimum distance of a linear code over a finite field ...
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Algebraic methods for the distance of cyclic codes
... In the scientific literature on the subject we can find two main competing ap- proaches in the determination of bounds for the distance, on which we elaborate below. The very first example of these bounds is the ...
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A generalized floor bound for the minimum distance of geometric Goppa codes
... error-correcting codes using two divisors on a curve. He also gives a distance bound based on the degrees of the ...actual minimum distance of the one-point Hermitian and certain one-point ...
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On the Computing of the Minimum Distance of Linear Block Codes by Heuristic Methods
... the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved ...
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Minimum Distance and Convergence Analysis of Hamming-Accumulate-Acccumulate Codes
... of codes formed by the serial concatenation of a Hamming code and two accumulate ...most codes in the ensemble have minimum distance growing linearly with the block ...resulting codes ...
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Cyclic Codes
... systematic cyclic codes Circuit for encoding systematic cyclic codes x x W We noticed earlier that e noticed earlier that cyclic codes can cyclic codes can be ...
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On an algorithm for classification of binary self-dual codes with minimum distance four
... self-dual codes for a given length is a quite interesting and challenging problem in coding ...inequivalent codes grows very fast with respect to the ...self-dual codes of length 36 by Harada and ...
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Minimum Edit Distance. Definition of Minimum Edit Distance
... I wanted to get across the idea that this was dynamic, this was multistage… I thought, let’s … take a word that has an absolutely precise meaning, namely dynamic… it’s impossible to us[r] ...
A note on reducing the computation time for minimum distance and equivalence check of binary linear codes
... the minimum distance of a linear code, and also efficient ways to check codes for equivalence when there are memory ...linear codes, self-dual codes, combinatorial designs and Gray ...
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Z_2-Triple Cyclic Codes and Their Duals
... Z 2 [x] hx r −1i × hx Z s 2 −1i [x] × hx Z t 2 −1i [x] , in polynomial representation. In this paper, we determine the structure of these codes. We have obtained the form of the generators for such codes. ...
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