Algebraic structure of quasicyclic codes
From MaRDI portal
Publication:5939242
DOI10.1016/S0166-218X(00)00350-4zbMath1023.94014MaRDI QIDQ5939242
Kristine Lally, Patrick Fitzpatrick
Publication date: 2 November 2003
Published in: Discrete Applied Mathematics (Search for Journal in Brave)
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Cyclic codes (94B15)
Related Items
Quasi-cyclic constructions of asymmetric quantum error-correcting codes, Optimal binary codes and binary construction of quantum codes, Quasi-cyclic constructions of quantum codes, On quasi-cyclic codes over \({\mathbb{Z}_q}\), Construction and decoding of matrix-product codes from nested codes, Unnamed Item, Multiplicative structure and Hecke rings of generator matrices for codes over quotient rings of Euclidean domains, One-Generator Quasi-Abelian Codes Revisited, Unnamed Item, Dual of codes over finite quotients of polynomial rings, Unnamed Item, Unnamed Item, Quasi-cyclic codes: algebraic properties and applications, On the algebraic structure of quasi-cyclic codes of index \(1\frac{1}{2} \), ON GENERALIZATIONS OF SKEW QUASI-CYCLIC CODES, Codes over affine algebras with a finite commutative chain coefficient ring, Unnamed Item, Codes over $\mathcal{L}(GF(2)^m,GF(2)^m)$, MDS Diffusion Matrices and Cryptographic Applications, Two-sided Galois duals of multi-twisted codes, Niederreiter cryptosystems using quasi-cyclic codes that resist quantum Fourier sampling, Constructing quasi-cyclic codes from linear algebra theory, On the generalised rank weights of quasi-cyclic codes, On Toeplitz codes of index \(t\) and isometry codes, A new construction of quantum codes from quasi-cyclic codes over finite fields, 1-generator quasi-cyclic codes, Quaternary 1-generator quasi-cyclic codes, Enumeration formulae for self-dual, self-orthogonal and complementary-dual quasi-cyclic codes over finite fields, Codes over finite quotients of polynomial rings, One-generator quasi-cyclic codes and their dual codes, A relation between quasi-cyclic codes and 2-D cyclic codes, New binary quantum stabilizer codes from the binary extremal self-dual \([48,24,12\) code], Quasi-cyclic codes as codes over rings of matrices, Quasi-abelian codes, On generator matrices and parity check matrices of generalized integer codes, On the algebraic structure of quasi-cyclic codes. IV: Repeated roots, Binary construction of pure additive quantum codes with distance five or six, On quasi-cyclic codes as a generalization of cyclic codes, Generalized quasi-cyclic codes: Structural properties and code construction, On self-orthogonal group ring codes, Quantum codes derived from one-generator quasi-cyclic codes with Hermitian inner product, Squares of matrix-product codes, Quaternary quasi-cyclic codes, On generator and parity-check polynomial matrices of generalized quasi-cyclic codes, New quasi-cyclic codes over \({\mathbb F}_{5}\), Skew G-codes
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A Gröbner basis technique for Padé approximation
- Optimal ternary quasi-cyclic codes
- On the scalar rational interpolation problem
- On the structure of Hermitian codes
- Solving a multivariable congruence by change of term order
- Structural properties and enumeration of quasi cyclic codes
- A (105,10,47) binary quasi-cyclic code
- New good rate \((m-1)/pm\) ternary and quaternary quasi-cyclic codes
- On behaviors and convolutional codes
- The trace description of irreducible quasi-cyclic codes
- A Connection Between Block and Convolutional Codes
- A transform theory for a class of group-invariant codes
- Nine good rate (m-1)/pm quasi-cyclic codes
- Some best rate 1/p and rate (p-1)/p systematic quasi-cyclic codes over GF(3) and GF(4)
- A Gilbert-Varshamov bound for quasi-cycle codes of rate 1/2 (Corresp.)
- On quasi-cyclic codes with rate l m (Corresp.)
- Twelve good rate (m-r)/pm quasi-cyclic codes
- Lifting standard bases in filtered structures
- On the key equation
- Self-orthogonal quasi-cyclic codes
- New binary coding results by circulants
- Some results on quasi-cyclic codes
- Decoding of circulant codes (Corresp.)
