Introduction to finite fields and their applications
Introduction to finite fields and their applications
The Correction Capability of the Berlekamp–Massey–Sakata Algorithm with Majority Voting
Applicable Algebra in Engineering, Communication and Computing
Improved geometric Goppa codes. I. Basic theory
IEEE Transactions on Information Theory - Part 1
Footprints or generalized Bezout's theorem
IEEE Transactions on Information Theory
On codes from norm-trace curves
Finite Fields and Their Applications
On the Structure of Order Domains
Finite Fields and Their Applications
Finite Fields and Their Applications
IEEE Transactions on Information Theory
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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 normtrace 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.