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2015 IEEE International Symposium on Information Theory (ISIT), 2015
Arikan introduced polar codes in 2009 and proved that they achieve the symmetric capacity, under low-complexity successive cancellation decoding, of any binary-input discrete memoryless channel. Arikan's construction is based on the Kronecker product of 2-by-2 matrices and it was extended to larger matrices by Sasoglu et al. in 2010.
Narayanan Rengaswamy, Henry D. Pfister
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Arikan introduced polar codes in 2009 and proved that they achieve the symmetric capacity, under low-complexity successive cancellation decoding, of any binary-input discrete memoryless channel. Arikan's construction is based on the Kronecker product of 2-by-2 matrices and it was extended to larger matrices by Sasoglu et al. in 2010.
Narayanan Rengaswamy, Henry D. Pfister
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2013 IEEE International Symposium on Information Theory, 2013
This paper considers cyclic DNA codes of arbitrary length over the ring R = F2[u]/(u4 - 1). A mapping is given between the elements of R and the alphabet {A, C, G, T} which allows the additive stem distance to be extended to this ring. Then, cyclic codes over R are designed such that their images under the mapping are also cyclic or quasi-cyclic of ...
Kenza Guenda +2 more
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This paper considers cyclic DNA codes of arbitrary length over the ring R = F2[u]/(u4 - 1). A mapping is given between the elements of R and the alphabet {A, C, G, T} which allows the additive stem distance to be extended to this ring. Then, cyclic codes over R are designed such that their images under the mapping are also cyclic or quasi-cyclic of ...
Kenza Guenda +2 more
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IEEE Transactions on Information Theory, 1965
A new class of cyclic codes, cyclic product codes, is characterized. These codes enjoy the implementation advantages of cyclic codes and, in addition, possess the important structural properties of product (iterated) codes. The main results are as follows: \begin{enumerate} \item Conditions are given which ensure that the product of two, and, hence ...
H. C. Burton, Edward J. Weldon Jr.
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A new class of cyclic codes, cyclic product codes, is characterized. These codes enjoy the implementation advantages of cyclic codes and, in addition, possess the important structural properties of product (iterated) codes. The main results are as follows: \begin{enumerate} \item Conditions are given which ensure that the product of two, and, hence ...
H. C. Burton, Edward J. Weldon Jr.
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IEEE Transactions on Information Theory, 2013
In this paper, the minimum weight and the dimension of all cyclic codes of length pn over a field Fq, are computed, when p is an odd prime and Fq a finite field with q elements, assuming that Fq generates the group of invertible elements of Zpn. Furthermore, the minimum weight and dimension of codes which are sum of two minimal codes in Fq(Cp×Cp) are ...
César Polcino Milies +1 more
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In this paper, the minimum weight and the dimension of all cyclic codes of length pn over a field Fq, are computed, when p is an odd prime and Fq a finite field with q elements, assuming that Fq generates the group of invertible elements of Zpn. Furthermore, the minimum weight and dimension of codes which are sum of two minimal codes in Fq(Cp×Cp) are ...
César Polcino Milies +1 more
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Journal of Cybernetics, 1976
In this paper the phasing aspects are considered in terms of cyclic blocks so that a code word is composed of several blocks, each block having a cyclic structure. The theory is analogically developed as in the classical case.
Sharma, B. D., Kaur, Bhupinder
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In this paper the phasing aspects are considered in terms of cyclic blocks so that a code word is composed of several blocks, each block having a cyclic structure. The theory is analogically developed as in the classical case.
Sharma, B. D., Kaur, Bhupinder
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44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings., 2004
Cyclic linear codes of block length n over a finite field F/sub q/ are linear subspaces of F/sub q//sup n/ that are invariant under a cyclic shift of their coordinates. A family of codes is good if all the codes in the family have constant rate and constant normalized distance (distance divided by block length).
László Babai +2 more
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Cyclic linear codes of block length n over a finite field F/sub q/ are linear subspaces of F/sub q//sup n/ that are invariant under a cyclic shift of their coordinates. A family of codes is good if all the codes in the family have constant rate and constant normalized distance (distance divided by block length).
László Babai +2 more
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IEEE Transactions on Information Theory, 1967
A subclass of cyclic codes of composite block length n=n' \cdot n" , with n' and n" relatively prime, is studied. It is shown how, under certain conditions, these codes may be factorized into subcodes of block length n' and n" and how they are related to codes of block length n' or n" , over extension fields of the base field.
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A subclass of cyclic codes of composite block length n=n' \cdot n" , with n' and n" relatively prime, is studied. It is shown how, under certain conditions, these codes may be factorized into subcodes of block length n' and n" and how they are related to codes of block length n' or n" , over extension fields of the base field.
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The genetic code and cyclic codes.
Comptes rendus de l'Academie des sciences. Serie III, Sciences de la vie, 1983We proposed previously a cyclic code made of 22 triplets, which we now call the AB code. It is made up of the following chain: AUGGUGCCAUUCAAGACUAUGA. The letters A, U, C, G represent the classical symbols of the (purine and pyrimidine) bases of the genetic code.
J, Demongeot, J, Besson
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Discrete Mathematics
BCH codes are a subclass of cyclic codes with many interesting properties. Over the last sixty years, a lot of progress has been made in the study of BCH codes. This survey paper presents the state-of-the-art of BCH cyclic codes and their applications.
Ding, Cunsheng, Li, Chengju
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BCH codes are a subclass of cyclic codes with many interesting properties. Over the last sixty years, a lot of progress has been made in the study of BCH codes. This survey paper presents the state-of-the-art of BCH cyclic codes and their applications.
Ding, Cunsheng, Li, Chengju
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1971
We now introduce a set of multiple-error correcting codes which were discovered by R. C. Bose and D. K. Ray-Chaudhuri and independently by A. Hocquenghem and which are now known as BCH-codes.
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We now introduce a set of multiple-error correcting codes which were discovered by R. C. Bose and D. K. Ray-Chaudhuri and independently by A. Hocquenghem and which are now known as BCH-codes.
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