scholarly journals New bounds for codes over finite Frobenius rings

2010 ◽  
Vol 57 (2) ◽  
pp. 169-179 ◽  
Author(s):  
Eimear Byrne ◽  
Marcus Greferath ◽  
Axel Kohnert ◽  
Vitaly Skachek
Keyword(s):  
Frobenius Rings ◽  
Finite Frobenius Rings

ON PLOTKIN-OPTIMAL CODES OVER FINITE FROBENIUS RINGS

2006 ◽  
Vol 05 (06) ◽  
pp. 799-815 ◽  
Author(s):  
MARCUS GREFERATH ◽  
GARY McGUIRE ◽  
MICHAEL E. O'SULLIVAN
Keyword(s):  
Hadamard Matrices ◽  
Interesting Property ◽  
Optimal Codes ◽  
Frobenius Ring ◽  
Frobenius Rings ◽  
Plotkin Bound ◽  
Homogeneous Weight ◽  
Finite Frobenius Rings ◽  
Finite Frobenius Ring ◽  
The Relationship

We study the Plotkin bound for codes over a finite Frobenius ring R equipped with the homogeneous weight. We show that for codes meeting the Plotkin bound, the distribution on R induced by projection onto a coordinate has an interesting property. We present several constructions of codes meeting the Plotkin bound and of Plotkin-optimal codes. We also investigate the relationship between Butson–Hadamard matrices and codes over R meeting the Plotkin bound.

scholarly journals FINITE QUASI-FROBENIUS MODULES AND LINEAR CODES

2004 ◽  
Vol 03 (03) ◽  
pp. 247-272 ◽  
Author(s):  
MARCUS GREFERATH ◽  
ALEXANDR NECHAEV ◽  
ROBERT WISBAUER
Keyword(s):  
Finite Fields ◽  
Linear Codes ◽  
General Setting ◽  
Commutative Rings ◽  
Finite Ring ◽  
Weight Enumerators ◽  
Frobenius Rings ◽  
Finite Frobenius Rings

The theory of linear codes over finite fields has been extended by A. Nechaev to codes over quasi-Frobenius modules over commutative rings, and by J. Wood to codes over (not necessarily commutative) finite Frobenius rings. In the present paper, we subsume these results by studying linear codes over quasi-Frobenius and Frobenius modules over any finite ring. Using the character module of the ring as alphabet, we show that fundamental results like MacWilliams' theorems on weight enumerators and code isometry can be obtained in this general setting.

Characterization of finite Frobenius rings

2001 ◽  
Vol 76 (6) ◽  
pp. 406-415 ◽  
Author(s):  
T. Honold
Keyword(s):  
Frobenius Rings ◽  
Finite Frobenius Rings

scholarly journals Application of fast Fourier transform for solving of the LPN problem over finite frobenius rings

2017 ◽  
Vol 19 (4) ◽  
Author(s):  
Антон Миколайович Олексійчук ◽  
Сергій Михайлович Ігнатенко
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Frobenius Rings ◽  
Finite Frobenius Rings ◽  
Lpn Problem

scholarly journals Errata for “The linear programming bound for codes over finite Frobenius rings”

2007 ◽  
Vol 45 (2) ◽  
pp. 269-270
Author(s):  
Eimear Byrne ◽  
Marcus Greferath ◽  
Michael E. O’Sullivan
Keyword(s):  
Linear Programming ◽  
Linear Programming Bound ◽  
Frobenius Rings ◽  
Finite Frobenius Rings

Demi-matroids from codes over finite Frobenius rings

2013 ◽  
Vol 75 (1) ◽  
pp. 97-107 ◽  
Author(s):  
Thomas Britz ◽  
Keisuke Shiromoto ◽  
Thomas Westerbäck
Keyword(s):  
Frobenius Rings ◽  
Finite Frobenius Rings
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