Construction of binary and ternary self-orthogonal linear codes

Authors:
Axel Kohnert;Alfred Wassermann
Affiliations:
Mathematical Department, University of Bayreuth, D-95440 Bayreuth, Germany;Mathematical Department, University of Bayreuth, D-95440 Bayreuth, Germany
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 3
Cited 0

Error-Correcting Linear Codes: Classification by Isometry and Applications (Algorithms and Computation in Mathematics)

Error-Correcting Linear Codes: Classification by Isometry and Applications (Algorithms and Computation in Mathematics)
Construction of linear codes with large minimum distance

IEEE Transactions on Information Theory
Optimal linear codes from matrix groups

IEEE Transactions on Information Theory

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Abstract

We construct new binary and ternary self-orthogonal linear codes. In order to do this we use an equivalence between the existence of a self-orthogonal linear code with a prescribed minimum distance and the existence of a solution of a certain system of Diophantine linear equations. To reduce the size of the system of equations we restrict the search for solutions to solutions with special symmetry given by matrix groups. Using this method we found at least six new distance-optimal codes, which are all self-orthogonal.