Document Type: Article All Authors / Contributors: M Barbier; C Chabot; G Quintin ISSN:1071-5797 BL Shelfmark:3928.326000 Language Note: English Unique Identifier: 809741653 Awards:
| Title | : | On quasi-cyclic codes as a generalization of cyclic codes |
| Author | : | M Barbier; C Chabot; G Quintin |
| Language | : | en |
| Rating | : | 4.90 out of 5 stars |
| Type | : | PDF, ePub, Kindle |
| Uploaded | : | Apr 12, 2021 |
Full Download On quasi-cyclic codes as a generalization of cyclic codes - M Barbier; C Chabot; G Quintin | PDF
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Abstract: construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic codes, we provide quasi-cyclic extended constructions that preserve the self-orthogonality to obtain stabilizer quantum codes.
Further, we study quasi-cyclic codes as orbit codes in the grassmannian parameterizing constant dimension codes.
Currently there exist two public-key cryptosystems based upon quasi-cyclic codes. The first proposal uses subcodes of a primitive bch cyclic code. The size of the public key for this cryptosystem is about 20kbits. The other one tries to combine these two positive aspects by requiring quasi-cyclic ldpc codes. It also avoids trivial attacks against mceliece type cryptosystems based on ldpc codes by using in the secret key a more general kind of invertible matrix instead of a permutation matrix.
Quantum codes detecting single bit-flip error can be derived from the constructed codes. Keywords: generalized skew quasi-cyclic codes, skew polynomial.
In this correspondence we present a special class of quasi-cyclic low-density parity-check (qc-ldpc) codes, called block-type ldpc (b-ldpc) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a qc-ldpc code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed ldpc codes.
On the algebraic structure of quasi-cyclic codes i: finite fields.
In this paper, we investigate quasi-cyclic codes over the ring. We investigate the structure of generators for one-generator.
Abstract—the encoding complexity of a general ( en,ek) quasi-cyclic code is o(e2(n−k)k). This paper presents a novel low-complexity encoding algorithm for quasi-cyclic (qc) codesbased on matrix transformation. First, a message vector is encoded into a transformed codeword in the transform domain.
Of ldpc codes, quasi-cyclic (qc) ldpc codes are well suited to hardware implementation because of the regularity in parity check matrices. In addition, qc-ldpc codes can provide comparable error-correction performance compared with random ldpc codes [17], [18].
Quasi-cyclic (qc) codes are a generalization of cyclic codes whereby a cyclic shift of a codeword by p positions results in another codeword. A circulant matrix is defined to be a square matrix c of the form.
The design of a practical code-based signature scheme is an open problem in efficient one-time signatures from quasi-cyclic codes: a full treatment.
Abstract: it has been well-known that the class of quasi-cyclic (qc) codes contain many good keywords: binary linear codes, quasi-cyclic codes, algorithms.
We investigate the structure of generalized quasi cyclic (gqc) codes. We determine the generator of 1-generator gqc codes and prove a bch type bound.
Quasi-cyclic codes form an important class of algebraic codes that includes cyclic codes as a special subclass. This chapter focuses on the algebraic structure of quasi-cyclic codes, first.
Quasi-cyclic codes which are cyclic up to equivalence can then be studied using the knowledge of cyclic codes. In this paper, we follow natividad’s approach and develop a similar result for the case where c is a quasi-cyclic code of length m and index over a finite field f with m coprime to both.
Quasi-cyclic codes form a generalization of cyclic codes, and contain a large number of record breaking codes. In this paper, we provide a method for constructing self-orthogonal quasi-cyclic codes, and obtain a large number of new quantum quasi-cyclic codes by css construction.
May 6, 2017 cyclic codes have some additional structural constraint on the codes. They are based on galois fields and because of their structural properties.
The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring.
Oct 15, 2020 pdf previously, (linear) codes over z 4 and quasi-cyclic (qc) codes (over fields ) have been shown to yield useful results in coding theory.
Cyclic quadrilaterial with questions types types of questions questions types in probability questions types on probability questions types on linear.
A new lower bound on the minimum hamming distance of linear quasi-cyclic codes over finite fields is proposed. It is based on spectral analysis and generalizes the semenov-trifonov bound in a similar way as the hartmann-tzeng bound extends the bch approach for cyclic codes. Furthermore, a syndrome-based algebraic decoding algorithm is given.
I will try to find a sufficient and necessary conditions so any permuted quasi cyclic code can be written as a matrix product of those codes. Another generalization of cyclic codes is the family of multi cyclic codes.
Quasi-cyclic (qc) codes a re an important class of linear co des and have some good algebra structures [3]-[10]. Rece ntly there a re some research pap ers about q c codes over finite.
Most of the works have concentrated on the algebraic-combinatorial computers search ([5]-[8]).
Abstract: following parts i and ii, quasi-cyclic codes of given index are studied as codes over a finite polynomial ring. These latter codes are decomposed by the chinese remainder theorem (crt), or equivalently the mattson-solomon transform, into products of shorter codes over larger alphabets. We characterize and enumerate self-dual one-generator quasi-cyclic codes in that context.
Leiner, “ldpc codes – a brief tutorial”, april- 2005 jingyu kang, qin huang, li zhang, bo zhou, and shu lin, “quasi-cyclic ldpc codes: an algebraic construction”, ieee trans. 5, may 2010 qiao guo-lei and dong zi-jian, “design of structured ldpc codes with quasi-cyclic and rotation architecture.
Quasi-cyclic (qc) ldpc codes play an important role in 5g communications and have been chosen as the standard codes for 5g enhanced mobile broadband (embb) data channel. In this paper, we study the construction of qc ldpc codes based on an arbitrary given expansion factor (or lifting degree).
An (,) quasi-cyclic code is a linear block code such that, for some which is coprime to the polynomial () (−) is a codeword polynomial whenever () is a codeword polynomial. Here, codeword polynomial is an element of a linear code whose code words are polynomials that are divisible by a polynomial of shorter length called the generator polynomial.
We propose two new cryptosystems instantiated within our framework: the hamming quasi-cyclic.
We study and enumerate cyclic codes which include generalised reed-solomon codes as function field codes.
Fingerprint dive into the research topics of 'ldpc codes derived from quasi-cyclic code design suitable for optical communications'.
This talk is based on joint work with san ling (ntu, singapore) on quasi cyclic.
Abstract: a new class of linear block codes, called self-orthogonal quasi-cyclic codes, is defined. It is shown that the problem of designing these codes is equivalent to the problem of designing disjoint difference sets. As a result, several classes of optimal and near-optimal codes can be constructed analytically and other codes can be found by a computer-aided search procedure.
Chapter a quasi-cyclic codes as cyclic codes over a family of local rings. Chapter b z2z4-additive cyclic codes, generator polynomials and dual codes.
On the algebraic structure of quasi-cyclic codes i: finite fields san ling and patrick solé, member, ieee abstract— a new algebraic approach to quasi-cyclic codes is in-troduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring.
A quantum-secure niederreiter cryptosystem using quasi-cyclic codes. In this paper, we describe a new niederreiter cryptosystem based on quasi-cyclic codes that is quantum-secure. This new cryptosystem has good transmission rate compared to the one using binary goppa codes and uses smaller keys.
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