Simplex code - Open Access .click

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
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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.
H J Landau, David Slepian
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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
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