2010, 4(3): 363-367. doi: 10.3934/amc.2010.4.363

New linear codes from matrix-product codes with polynomial units

1. 

Department of Mathematics, University College Cork, Cork, Ireland

2. 

Department of Mathematical Sciences, Aalborg University, 9220-Aalborg Øst, Denmark

Received  November 2009 Revised  February 2010 Published  August 2010

A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.
Citation: Fernando Hernando, Diego Ruano. New linear codes from matrix-product codes with polynomial units. Advances in Mathematics of Communications, 2010, 4 (3) : 363-367. doi: 10.3934/amc.2010.4.363
[1]

Fernando Hernando, Tom Høholdt, Diego Ruano. List decoding of matrix-product codes from nested codes: An application to quasi-cyclic codes. Advances in Mathematics of Communications, 2012, 6 (3) : 259-272. doi: 10.3934/amc.2012.6.259

[2]

Michael Kiermaier, Johannes Zwanzger. A $\mathbb Z$4-linear code of high minimum Lee distance derived from a hyperoval. Advances in Mathematics of Communications, 2011, 5 (2) : 275-286. doi: 10.3934/amc.2011.5.275

[3]

Irene Márquez-Corbella, Edgar Martínez-Moro, Emilio Suárez-Canedo. On the ideal associated to a linear code. Advances in Mathematics of Communications, 2016, 10 (2) : 229-254. doi: 10.3934/amc.2016003

[4]

Laura Luzzi, Ghaya Rekaya-Ben Othman, Jean-Claude Belfiore. Algebraic reduction for the Golden Code. Advances in Mathematics of Communications, 2012, 6 (1) : 1-26. doi: 10.3934/amc.2012.6.1

[5]

Serhii Dyshko. On extendability of additive code isometries. Advances in Mathematics of Communications, 2016, 10 (1) : 45-52. doi: 10.3934/amc.2016.10.45

[6]

Olof Heden. The partial order of perfect codes associated to a perfect code. Advances in Mathematics of Communications, 2007, 1 (4) : 399-412. doi: 10.3934/amc.2007.1.399

[7]

Selim Esedoḡlu, Fadil Santosa. Error estimates for a bar code reconstruction method. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1889-1902. doi: 10.3934/dcdsb.2012.17.1889

[8]

M. Delgado Pineda, E. A. Galperin, P. Jiménez Guerra. MAPLE code of the cubic algorithm for multiobjective optimization with box constraints. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 407-424. doi: 10.3934/naco.2013.3.407

[9]

Andrew Klapper, Andrew Mertz. The two covering radius of the two error correcting BCH code. Advances in Mathematics of Communications, 2009, 3 (1) : 83-95. doi: 10.3934/amc.2009.3.83

[10]

Masaaki Harada, Takuji Nishimura. An extremal singly even self-dual code of length 88. Advances in Mathematics of Communications, 2007, 1 (2) : 261-267. doi: 10.3934/amc.2007.1.261

[11]

José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro. Information--bit error rate and false positives in an MDS code. Advances in Mathematics of Communications, 2015, 9 (2) : 149-168. doi: 10.3934/amc.2015.9.149

[12]

José Joaquín Bernal, Diana H. Bueno-Carreño, Juan Jacobo Simón. Cyclic and BCH codes whose minimum distance equals their maximum BCH bound. Advances in Mathematics of Communications, 2016, 10 (2) : 459-474. doi: 10.3934/amc.2016018

[13]

M. De Boeck, P. Vandendriessche. On the dual code of points and generators on the Hermitian variety $\mathcal{H}(2n+1,q^{2})$. Advances in Mathematics of Communications, 2014, 8 (3) : 281-296. doi: 10.3934/amc.2014.8.281

[14]

Sihuang Hu, Gabriele Nebe. There is no $[24,12,9]$ doubly-even self-dual code over $\mathbb F_4$. Advances in Mathematics of Communications, 2016, 10 (3) : 583-588. doi: 10.3934/amc.2016027

[15]

Anna-Lena Horlemann-Trautmann, Kyle Marshall. New criteria for MRD and Gabidulin codes and some Rank-Metric code constructions. Advances in Mathematics of Communications, 2017, 11 (3) : 533-548. doi: 10.3934/amc.2017042

[16]

Masaaki Harada, Ethan Novak, Vladimir D. Tonchev. The weight distribution of the self-dual $[128,64]$ polarity design code. Advances in Mathematics of Communications, 2016, 10 (3) : 643-648. doi: 10.3934/amc.2016032

[17]

Denis S. Krotov, Patric R. J.  Östergård, Olli Pottonen. Non-existence of a ternary constant weight $(16,5,15;2048)$ diameter perfect code. Advances in Mathematics of Communications, 2016, 10 (2) : 393-399. doi: 10.3934/amc.2016013

[18]

Jianying Fang. 5-SEEDs from the lifted Golay code of length 24 over Z4. Advances in Mathematics of Communications, 2017, 11 (1) : 259-266. doi: 10.3934/amc.2017017

[19]

Martino Borello, Francesca Dalla Volta, Gabriele Nebe. The automorphism group of a self-dual $[72,36,16]$ code does not contain $\mathcal S_3$, $\mathcal A_4$ or $D_8$. Advances in Mathematics of Communications, 2013, 7 (4) : 503-510. doi: 10.3934/amc.2013.7.503

[20]

Heide Gluesing-Luerssen, Fai-Lung Tsang. A matrix ring description for cyclic convolutional codes. Advances in Mathematics of Communications, 2008, 2 (1) : 55-81. doi: 10.3934/amc.2008.2.55

2017 Impact Factor: 0.564

Metrics

  • PDF downloads (3)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]