On the subfield subcodes of Hermitian codes |
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| Authors: | Fernando Piñero Heeralal Janwa |
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| Institution: | 1. Department of Mathematics, Technical University of Denmark, 2800, Lyngby, Denmark
2. Department of Mathematics, University of Puerto Rico-Rio Piedras, P.O. Box 70377, San Juan, PR, 00936-8377, USA
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| Abstract: | We present a fast algorithm using Gröbner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤ 32 and length up to 215. We show that some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and we show the existence of good long codes. |
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