Results 231 to 240 of about 9,296 (263)

Hulls of linear codes from simplex codes

Designs, Codes, and Cryptography, 2023
Let \(C\) be a linear \([n,k,d]\)-code over the finite field \(\mathbb{F}_q\). There are at least two natural inner products defined in the vector space \(\mathbb{F}_q^n\), namely Euclidean as well as Hermitian inner products. Let \(C^{\perp_E}\) and \(C^{\perp_H}\) denote Euclidean and Hermitian dual of the code \(C\), respectively. Let \(\mathrm{Hull}
Guangkui Xu, Gaojun Luo, Xiwang Cao
exaly   +3 more sources

On the covering radius of Simplex codes

Journal of Discrete Mathematical Sciences and Cryptography, 2003
Abstract Lower and upper bounds for R(Sk (q)), the covering radius of a k-dimensional q-ary Simplex codes are determined. These help in getting bounds with a gap of one for S 3(q). Exact covering radius of S 2(q), S 3 (3), S 4(3), S 4 (4) and S 3(q) for q even are obtained.
M. C. Bhandari, C. Durairajan
exaly   +2 more sources

The Simplex Codes and Other Even-Weight Binary Linear Codes for Error Correction

IEEE Transactions on Information Theory, 2004
The probability of correct decoding on the binary-symmetric channel is studied. In particular, a class of codes with the same lengths and dimensions as the linear simplex codes, but with larger probability of correct decoding for all parameters p, 0 < p < 1/2, is given.
T Helleseth, T Klove, V I Levenshtein
exaly   +2 more sources

On some punctured codes of ℤq-Simplex codes

Discrete Mathematics, Algorithms and Applications, 2021
In this paper, we have constructed some new codes from [Formula: see text]-Simplex code called unit [Formula: see text]-Simplex code. In particular, we find the parameters of these codes and have proved that it is a [Formula: see text] [Formula: see text]-linear code, where [Formula: see text] and [Formula: see text] is a smallest prime divisor of ...
J. Prabu, J. Mahalakshmi, C. Durairajan 0001, S. Santhakumar   +3 more
openaire   +1 more source

Optimization of SNR improvement in the noncoherent OTDR based on simplex codes

Journal of Lightwave Technology, 2006
This paper demonstrates signal-to-noise ratio (SNR) improvement of an optical time-domain reflectometer (OTDR) using simplex codes (scs) for the first time.
Hosung Yoon, Pilhan Kim, Namkyoo Park
exaly   +2 more sources

On the Optimality of the Regular Simplex Code

Bell System Technical Journal, 1966
We prove here the long conjectured fact that the regular simplex is the code of minimal error probability for transmission over the infinite-band Gaussian channel. The code is actually optimal for a rather wide class of assumed channel noises. We also establish the optimality of several other codes for the band-limited Gaussian channel.
Landau, H. J., Slepian, D.
openaire   +1 more source

New Constructions of Symbol-Pair Simplex Codes

IEEE Transactions on Information Theory
Zihui Liu
exaly   +2 more sources

Some new constructions for simplex codes

IEEE Transactions on Information Theory, 1994
Summary: Three constructions for \(n\)-dimensional regular simplex codes \(\alpha_ i\), \(0\leq i\leq n\), are proposed, two of which have the property that \(\alpha_ i\) for \(1\leq i\leq n\) is a cyclic shift of \(\alpha_ 1\). The first method is shown to work for all the positive integers \(n=1,2,\dots\) using only three real values.
Hong-Yeop Song, Solomon W. Golomb
openaire   +1 more source

On Senary Simplex Codes

2001
This paper studies senary simplex codes of type ? and two punctured versions of these codes (type s and ?). Self-orthogonality, torsion codes, weight distribution and weight hierarchy properties are studied. We give a new construction of senary codes via their binary and ternary counterparts, and show that type ?
Manish K. Gupta 0004, David G. Glynn, T. Aaron Gulliver   +2 more
openaire   +1 more source

On simplex-type binary codes

IEEE Trans. Inf. Theory, 1982
The rank of the generating matrix in certain cases is computed. The result is perhaps of interest in its own right, apart from any applications it may have. The method of proof, utilizing as it does a knowledge of the parameters of a certain association scheme, is a technique which can be profitably used elsewhere.
openaire   +2 more sources