Results 261 to 270 of about 113,006 (300)

The poset structures admitting the extended binary Hamming code to be a perfect code

Discrete Mathematics, 2004
Brualdi et al. introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Hamming code to be a double-error-correcting perfect P-code. Our study is motivated by this example.
Jong Yoon Hyun, Hyun Kwang Kim
exaly   +3 more sources

Perfect Code is W[1]-complete

Information Processing Letters, 2002
We show that the parameterized problem Perfect Code belongs to W[1]. This result closes an old open question, because it was often conjectured that Perfect Code could be a natural problem having complexity degree intermediate between W[1] and W[2].
Marco Cesati
exaly   +2 more sources

A Full Rank Perfect Code of Length 31

Designs, Codes, and Cryptography, 2006
A full rank perfect 1-error correcting binary code of length 31 with a kernel of dimension 21 is described. This was the last open case of the rank-kernel problem of Etzion and Vardy.
Olof Héden
exaly   +2 more sources

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Nonsystematic perfect codes

SIAM Journal on Discrete Mathematics, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kevin T. Phelps, Mike LeVan
openaire   +1 more source

Low Complexity Decoding of the 4×4 Perfect Space-time Block Code

Procedia Computer Science, 2014
The 4x4 perfect space-time block code (STBC) is one type in a family of perfect STBCs that have full rate, full diversity, a non- vanishing constant minimum determinant that improves spectral efficiency, uniform average transmitted energy per antenna ...
Elie Amani, Karim Djouani, Anish Kurien   +2 more
exaly   +2 more sources

The Classification of Some Perfect Codes

Designs, Codes and Cryptography, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sergey V. Avgustinovich, Olof Heden, Faina I. Solov'eva   +2 more
openaire   +1 more source

On Perfect Codes: Rank and Kernel

Designs, Codes and Cryptography, 2002
The rank of a nonlinear binary code \(C\) is the dimension of the subspace spanned by \(C\). The kernel of \(C\) is the largest possible linear code \(C'\) such that \(C\) can be obtained as a union of cosets of \(C'\). The authors study the problem of determining for what parameters \((r,k)\) there exists a perfect binary one-error-correcting code of ...
Kevin T. Phelps, Mercè Villanueva
openaire   +1 more source

On Perfect Codes and Related Concepts

Designs, Codes and Cryptography, 2001
The concept of diameter perfect codes, which is a natural generalization of perfect codes (codes attaining the sphere-packing or Hamming bound), is introduced. The motivation for this work comes from the ``code-anticode'' bound of Delsarte in distance regular graphs.
Ahlswede, Rudolf, Aydinian, Haratyun, Khachatrian, Levon H.   +2 more
openaire   +1 more source

There exist Steiner triple systems of order 15 that do not occur in a perfect binary one-error-correcting code

Journal of Combinatorial Designs, 2007
The codewords at distance three from a particular codeword of a perfect binary one-error-correcting code (of length 2m - 1) form a Steiner triple system.
Patric R J Ostergard, Olli Pottonen
exaly   +2 more sources

On perfect integer codes

Proceedings. International Symposium on Information Theory, 2005. ISIT 2005., 2005
A general construction for perfect integer codes is provided, which allows to efficiently compute such codes. The method is applied to investigate in detail the special error set {plusmn1, plusmna, plusmnb, plusmnc,} interesting for single error correction of peak shifts and codes defined on ...
openaire   +1 more source