A linear construction for certain Kerdock and Preparata codes
From MaRDI portal
Publication:4275679
DOI10.1090/S0273-0979-1993-00426-9zbMath0783.94026arXivmath/9310227OpenAlexW2081059897MaRDI QIDQ4275679
Robert Calderbank, N. J. A. Sloane, A. Roger Jun. Hammons, P. Vijay Kumar, Patrick Solé
Publication date: 21 January 1994
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/9310227
Related Items (47)
Duality preserving Gray maps for codes over rings ⋮ Repeated-root constacyclic codes of prime power length over \(\frac{\mathbb{F}_{p^m} [u}{\langle u^a \rangle}\) and their duals] ⋮ Roulette games and depths of words over finite commutative rings ⋮ On the structure of cyclic codes over the ring \(\mathbb{Z}_{2^s} [u/\langle u^k \rangle\)] ⋮ Negacyclic codes over the local ring \(\mathbb{Z}_4 [v / \langle v^2 + 2 v \rangle\) of oddly even length and their gray images] ⋮ On the enumeration and classification of \(\sigma\)-LCD codes over finite commutative chain rings ⋮ Repeated-root constacyclic codes of arbitrary lengths over the Galois ring GR(p2,m) ⋮ On \(\sigma \)-self-orthogonal constacyclic codes over \(\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}\) ⋮ Repeated-root constacyclic codes of prime power lengths over finite chain rings ⋮ On structure and distances of some classes of repeated-root constacyclic codes over Galois rings ⋮ Constacyclic codes of length \(p^s\) over \(\mathbb F_{p^m} + u\mathbb F_{p^m}\) ⋮ Complete classification for simple root cyclic codes over the local ring \(\mathbb{Z}_4[v/\langle v^2+2v\rangle \)] ⋮ Unnamed Item ⋮ Frobenius-Artin algebras and infinite linear codes ⋮ On self-dual constacyclic codes of length \(p^s\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\) ⋮ 2-modular lattices from ternary codes. ⋮ On the symbol-pair distance of some classes of repeated-root constacyclic codes over Galois ring ⋮ Constacyclic codes of length \(2p^{s}\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\) ⋮ Construction and enumeration of self-orthogonal and self-dual codes over Galois rings of even characteristic ⋮ Repeated-root constacyclic codes of length $2p^s$ over Galois rings ⋮ Hermitian self-dual codes over \(\mathbb F_{2^{2m}}+u\mathbb F_{2^{2m}}\) ⋮ A recursive method for the construction and enumeration of self-orthogonal and self-dual codes over the quasi-Galois ring \(\mathbb{F}_{2^r}[u/<u^e>\)] ⋮ Mass formulae for Euclidean self-orthogonal and self-dual codes over finite commutative chain rings ⋮ Negacyclic codes of length \(2p^s\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\) ⋮ On the covering radius of some modular codes ⋮ Unnamed Item ⋮ On codes over ℤp2 and its covering radius ⋮ Non-invertible-element constacyclic codes over finite PIRs ⋮ Lee distance of cyclic and \((1 + u\gamma)\)-constacyclic codes of length \(2^s\) over \(\mathbb{F}_{2^m} + u \mathbb{F}_{2^m} \) ⋮ Constructions of self-dual codes and formally self-dual codes over rings ⋮ Left dihedral codes over Galois rings \(\mathrm{GR}(p^2, m)\) ⋮ On constacyclic codes of length \(4p^s\) over \(\mathbb{F}_{p^m} +u\mathbb{F}_{p^m}\) ⋮ Homogeneous metric and matrix product codes over finite commutative principal ideal rings ⋮ Additive cyclic codes over finite commutative chain rings ⋮ RT distance and weight distributions of Type 1 constacyclic codes of length 4ps over Fpm[u] ⋮ Construction of extremal self-dual codes over \(\mathbb F_2+u\mathbb F_2\) with an automorphism of odd order ⋮ Cyclic codes over the ring \(\mathrm{GR}(p^e, m) [u / \langle u^k \rangle \)] ⋮ Hulls of cyclic codes over \(\mathbb{Z}_4\) ⋮ Repeated-root constacyclic codes of length \(2p^s\) over \(\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m} \) ⋮ Lee-extremal self-dual codes over \(\mathbb{F}_2 + u \mathbb{F}_2\) of lengths 23 and 24 ⋮ Unnamed Item ⋮ REPEATED-ROOT CONSTACYCLIC CODES OVER F3+uF3+uvF3 ⋮ NETWORK CODING WITH MODULAR LATTICES ⋮ On the equivalence of codes over rings and modules ⋮ Duadic \(\mathbb{Z}_4\)-codes ⋮ Shadow codes over \({\mathbb Z}_4\) ⋮ Quaternary constructions for the binary single-error-correcting codes of Julin, Best and others
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Über die Identität von MacWilliams für die Gewichtsfunktion von Codes
- Self-dual codes over the integers modulo 4
- Alternating bilinear forms over GF(q)
- Distance-regular digraphs of girth 4 over an extension ring of Z/4Z
- A class of low-rate nonlinear binary codes
- An exponential number of generalized Kerdock codes
- Spreads, Translation Planes and Kerdock Sets. II
- On the Preparata and Goethals codes
- On the inequivalence of generalized Preparata codes
- Low-dimensional lattices. VI. Voronoi reduction of three-dimensional lattices
- 4-phase sequences with near-optimum correlation properties
- Nonlinear codes defined by quadratic forms over GF(2)
- The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
- An optimum nonlinear code
- A class of optimum nonlinear double-error-correcting codes
This page was built for publication: A linear construction for certain Kerdock and Preparata codes
