Abstract
We consider a generalization of the codes defined by norm and trace functions on finite fields introduced by Olav Geil. The codes in the new family still satisfy Geil’s duality properties stated for norm-trace codes. That is, it is easy to find a minimal set of parity checks guaranteeing correction of a given number of errors, as well as the set of monomials generating the corresponding code. Furthermore, we describe a way to find the minimal set of parity checks and the corresponding generating monomials guaranteeing correction at least of generic errors. This gives codes with even larger dimensions.
Part of this work is in the manuscript [1] submitted for publication.
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Bras-Amorós, M., O’Sullivan, M.E. (2007). Extended Norm-Trace Codes with Optimized Correction Capability. In: Boztaş, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_39
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DOI: https://doi.org/10.1007/978-3-540-77224-8_39
Publisher Name: Springer, Berlin, Heidelberg
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