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The Simplex Codes and Other Even-Weight Binary Linear Codes for Error Correction
IEEE Transactions on Information Theory, 2004The 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
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Rate-Adaptive LDPC Codes Obtained from Simplex Codes [PDF]
ICC 2023 - IEEE International Conference on Communications, 2023 In this paper we show that, when a binary primitive polynomial can be associated to a sparse Golomb ruler, the simplex code obtained by taking it as the code parity-check polynomial exhibits good distance properties and performance.
Massimo Battaglioni +3 more
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On some punctured codes of ℤq-Simplex codes
Discrete Mathematics, Algorithms and Applications, 2021In 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 +3 more
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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 +2 more
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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 +2 more
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Some new constructions for simplex codes
IEEE Transactions on Information Theory, 1994Summary: 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
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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.
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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.
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On ℤ4-Simplex Codes and Their Gray Images
1999In [7] Rains has shown that for any linear code C over Z4, dH, the minimum Hammimg distance of C and dL, the minimum Lee distance of C satisfy dH ≥ ⌈dL/2⌉. C is said to be of type α(β) if dH = ⌈dL/2⌉ (dH > ⌈dL/2⌉). In this paper we define Simplex codes of type α and β, namely, Skα and Skβ, respectively over Z4.
Mahesh C. Bhandari +2 more
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The graph of 4-ary simplex codes of dimension 2
Finite Fields and Their Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mariusz Kwiatkowski, Mark Pankov
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Evaluation of Simplex Codes for Photoacoustic Coded Excitation
2009In biomedical photoacoustics (PA) ultrasound is generated by laser irradiation of tissue. Usually, PA signals are generated by Nd:YAG lasers, but it would be attractive to use less expensive laser diodes instead. Although laser diodes exhibit low pulse energy, the pulse repetition frequency (PRF) of pulsed laser diodes is much higher than the PRF of Nd:
Martin P. Mienkina +5 more
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Structural Extension of Polar Codes via Simplex Kernels
IEEE Transactions on Communications, 2020In this paper, we introduce a structural extension method of polar codes as a new code modification method. Structural extension is a systematic method of generating additional codeword bits from the mother code by selecting intermediate bits obtained in the middle of the polar encoding. We start by studying simplex-extension from a $2\times 2$
Min Jang +4 more
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