A new construction of Algebraic Geometry code using Trace function

02/29/2020

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by   Nupur Patanker, et al.

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In this note, we give a construction of Algebraic-Geometry codes on algebraic function field F/ F_q using places of F (not necessarily of degree one) and trace functions from various extensions of F_q. We compute a bound on the dimension of this code. We also determine a bound on the minimum distance of this code in terms of B_r(F) ( the number of places of degree r in F), 1 ≤ r < ∞. This code is a generalization of the geometric Goppa code, with no restriction on the length of the code except the support condition on divisors defining the code. We obtained few quasi-cyclic codes over F_p as examples of these codes.