American Institute of Mathematical Sciences

Advanced
August  2011, 5(3): 543-546. doi: 10.3934/amc.2011.5.543

On linear equivalence and Phelps codes. Addendum

Olof Heden 1, and  Martin Hessler 2,

1. 

Department of Mathematics, KTH, S-100 44 Stockholm
2. 

Åbylundsgatan 46, S-582 36 Linköping, Sweden

Received  January 2011 Revised  May 2011 Published  August 2011

A new class of perfect 1-error correcting binary codes, so called RRH-codes, are identified, and it is shown that every such code is linearly equivalent to a perfect code obtainable by the Phelps construction.
Keywords: Phelps codes, Perfect codes, tilings..
Mathematics Subject Classification: Primary: 94B2.
Citation: Olof Heden, Martin Hessler. On linear equivalence and Phelps codes. Addendum. Advances in Mathematics of Communications, 2011, 5 (3) : 543-546. doi: 10.3934/amc.2011.5.543
References:
[1]

O. Heden and M. Hessler, On linear equivalence and Phelps codes,, Adv. Math. Commun., 4 (2010), 69.  doi: 10.3934/amc.2010.4.69.  Google Scholar

[2]

M. Hessler, Perfect codes as isomorphic spaces,, Discr. Math., 306 (2006), 1981.  doi: 10.1016/j.disc.2006.03.039.  Google Scholar

show all references

References:
[1]

O. Heden and M. Hessler, On linear equivalence and Phelps codes,, Adv. Math. Commun., 4 (2010), 69.  doi: 10.3934/amc.2010.4.69.  Google Scholar

[2]

M. Hessler, Perfect codes as isomorphic spaces,, Discr. Math., 306 (2006), 1981.  doi: 10.1016/j.disc.2006.03.039.  Google Scholar

[1]

Olof Heden, Martin Hessler. On linear equivalence and Phelps codes. Advances in Mathematics of Communications, 2010, 4 (1) : 69-81. doi: 10.3934/amc.2010.4.69
[2]

Olof Heden. A survey of perfect codes. Advances in Mathematics of Communications, 2008, 2 (2) : 223-247. doi: 10.3934/amc.2008.2.223
[3]

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
[4]

B. K. Dass, Namita Sharma, Rashmi Verma. Characterization of extended Hamming and Golay codes as perfect codes in poset block spaces. Advances in Mathematics of Communications, 2018, 12 (4) : 629-639. doi: 10.3934/amc.2018037
[5]

Markku Lehtinen, Baylie Damtie, Petteri Piiroinen, Mikko Orispää. Perfect and almost perfect pulse compression codes for range spread radar targets. Inverse Problems & Imaging, 2009, 3 (3) : 465-486. doi: 10.3934/ipi.2009.3.465
[6]

Olof Heden, Fabio Pasticci, Thomas Westerbäck. On the existence of extended perfect binary codes with trivial symmetry group. Advances in Mathematics of Communications, 2009, 3 (3) : 295-309. doi: 10.3934/amc.2009.3.295
[7]

Olof Heden, Denis S. Krotov. On the structure of non-full-rank perfect $q$-ary codes. Advances in Mathematics of Communications, 2011, 5 (2) : 149-156. doi: 10.3934/amc.2011.5.149
[8]

Helena Rifà-Pous, Josep Rifà, Lorena Ronquillo. $\mathbb{Z}_2\mathbb{Z}_4$-additive perfect codes in Steganography. Advances in Mathematics of Communications, 2011, 5 (3) : 425-433. doi: 10.3934/amc.2011.5.425
[9]

Olof Heden, Fabio Pasticci, Thomas Westerbäck. On the symmetry group of extended perfect binary codes of length $n+1$ and rank $n-\log(n+1)+2$. Advances in Mathematics of Communications, 2012, 6 (2) : 121-130. doi: 10.3934/amc.2012.6.121
[10]

Ettore Fornasini, Telma Pinho, Raquel Pinto, Paula Rocha. Composition codes. Advances in Mathematics of Communications, 2016, 10 (1) : 163-177. doi: 10.3934/amc.2016.10.163
[11]

Michael Braun. On lattices, binary codes, and network codes. Advances in Mathematics of Communications, 2011, 5 (2) : 225-232. doi: 10.3934/amc.2011.5.225
[12]

Alexis Eduardo Almendras Valdebenito, Andrea Luigi Tironi. On the dual codes of skew constacyclic codes. Advances in Mathematics of Communications, 2018, 12 (4) : 659-679. doi: 10.3934/amc.2018039
[13]

Joaquim Borges, Josep Rifà, Victor Zinoviev. Completely regular codes by concatenating Hamming codes. Advances in Mathematics of Communications, 2018, 12 (2) : 337-349. doi: 10.3934/amc.2018021
[14]

Srimathy Srinivasan, Andrew Thangaraj. Codes on planar Tanner graphs. Advances in Mathematics of Communications, 2012, 6 (2) : 131-163. doi: 10.3934/amc.2012.6.131
[15]

M. B. Paterson, D. R. Stinson, R. Wei. Combinatorial batch codes. Advances in Mathematics of Communications, 2009, 3 (1) : 13-27. doi: 10.3934/amc.2009.3.13
[16]

Noam Presman, Simon Litsyn. Recursive descriptions of polar codes. Advances in Mathematics of Communications, 2017, 11 (1) : 1-65. doi: 10.3934/amc.2017001
[17]

Sergio Estrada, J. R. García-Rozas, Justo Peralta, E. Sánchez-García. Group convolutional codes. Advances in Mathematics of Communications, 2008, 2 (1) : 83-94. doi: 10.3934/amc.2008.2.83
[18]

Kwankyu Lee. Decoding of differential AG codes. Advances in Mathematics of Communications, 2016, 10 (2) : 307-319. doi: 10.3934/amc.2016007
[19]

JiYoon Jung, Carl Mummert, Elizabeth Niese, Michael Schroeder. On erasure combinatorial batch codes. Advances in Mathematics of Communications, 2018, 12 (1) : 49-65. doi: 10.3934/amc.2018003
[20]

José Ignacio Iglesias Curto. Generalized AG convolutional codes. Advances in Mathematics of Communications, 2009, 3 (4) : 317-328. doi: 10.3934/amc.2009.3.317

2018 Impact Factor: 0.879

Tools

Metrics

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

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences