Reed–Muller and Kerdock Codes

A Course in Algebraic Error-Correcting Codes - Compact Textbooks in Mathematics ◽

10.1007/978-3-030-41153-4_9 ◽

2020 ◽

pp. 133-150

Author(s):

Simeon Ball

Keyword(s):

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Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets

Journal of Combinatorial Theory Series A ◽

10.1016/j.jcta.2008.07.002 ◽

2009 ◽

Vol 116 (2) ◽

pp. 434-448 ◽

Author(s):

Kanat Abdukhalikov ◽

Eiichi Bannai ◽

Sho Suda

Keyword(s):

Association Schemes ◽

Kerdock Codes ◽

Optimal Configurations ◽

Universally Optimal

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Note on the complete decoding of Kerdock codes

IEE Proceedings I Communications Speech and Vision ◽

10.1049/ip-i-2.1992.0004 ◽

1992 ◽

Vol 139 (1) ◽

pp. 24 ◽

Author(s):

M. Elia ◽

C. Losana ◽

F. Neri

Keyword(s):

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Kerdock codes for limited feedback MIMO systems

2008 IEEE International Conference on Acoustics, Speech and Signal Processing ◽

10.1109/icassp.2008.4518309 ◽

2008 ◽

Author(s):

Takao Inoue ◽

Robert W. Heath

Keyword(s):

Mimo Systems ◽

Limited Feedback ◽

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PD-sets for Z4-linear codes: Hadamard and Kerdock codes

2016 IEEE International Symposium on Information Theory (ISIT) ◽

10.1109/isit.2016.7541512 ◽

2016 ◽

Author(s):

Roland D. Barrolleta ◽

Merce Villanueva

Keyword(s):

Linear Codes ◽

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Kerdock Codes for Limited Feedback Precoded MIMO Systems

IEEE Transactions on Signal Processing ◽

10.1109/tsp.2009.2020761 ◽

2009 ◽

Vol 57 (9) ◽

pp. 3711-3716 ◽

Author(s):

Takao Inoue ◽

Robert W. Heath

Keyword(s):

Mimo Systems ◽

Limited Feedback ◽

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On Kerdock codes

Finite Fields: Theory, Applications and Algorithms - Contemporary Mathematics ◽

10.1090/conm/225/03217 ◽

1999 ◽

pp. 155-163 ◽

Author(s):

Claude Carlet

Keyword(s):

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On components of the Kerdock codes and the dual of the BCH code C1,3

Discrete Mathematics ◽

10.1016/j.disc.2019.111668 ◽

2020 ◽

Vol 343 (2) ◽

pp. 111668

Author(s):

I. Yu. Mogilnykh ◽

F.I. Solov’eva

Keyword(s):

Bch Code ◽

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Z4 -Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

Proceedings of the London Mathematical Society ◽

10.1112/s0024611597000403 ◽

1997 ◽

Vol 75 (2) ◽

pp. 436-480 ◽

Author(s):

AR Calderbank ◽

PJ Cameron ◽

WM Kantor ◽

JJ Seidel

Keyword(s):

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Symplectic spread-based generalized Kerdock codes

Designs Codes and Cryptography ◽

10.1007/s10623-006-9031-8 ◽

2006 ◽

Vol 42 (2) ◽

pp. 213-226 ◽

Author(s):

S. González ◽

C. Martínez ◽

I. F. Rúa

Keyword(s):

Kerdock Codes ◽

Symplectic Spread

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NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS

Glasgow Mathematical Journal ◽

10.1017/s0017089520000191 ◽

2020 ◽

Vol 62 (S1) ◽

pp. S186-S205 ◽

Author(s):

IGNACIO F. RÚA

Keyword(s):

Galois Field ◽

Binary Codes ◽

Kerdock Codes ◽

Finite Semifields ◽

AbstractSymplectic finite semifields can be used to construct nonlinear binary codes of Kerdock type (i.e., with the same parameters of the Kerdock codes, a subclass of Delsarte–Goethals codes). In this paper, we introduce nonbinary Delsarte–Goethals codes of parameters $(q^{m+1}\ ,\ q^{m(r+2)+2}\ ,\ {\frac{q-1}{q}(q^{m+1}-q^{\frac{m+1}{2}+r})})$ over a Galois field of order $q=2^l$ , for all $0\le r\le\frac{m-1}{2}$ , with m ≥ 3 odd, and show the connection of this construction to finite semifields.

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