Kaplan, N;
Petrow, I;
(2018)
Traces of hecke operators and refined weight enumerators of reed-solomon codes.
Transactions of the American Mathematical Society
, 370
(4)
pp. 2537-2561.
10.1090/tran/7089.
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Abstract
We study the quadratic residue weight enumerators of the dual projective Reed-Solomon codes of dimensions 5 and q − 4 over the finite field Fq. Our main results are formulas for the coefficients of the the quadratic residue weight enumerators for such codes. If q = p v and we fix v and vary p then our formulas for the coefficients of the dimension q − 4 code involve only polynomials in p and the trace of the q th and (q/p2 ) th Hecke operators acting on spaces of cusp forms for the congruence groups SL2(Z), Γ0(2), and Γ0(4). The main tool we use is the Eichler-Selberg trace formula, which gives along the way a variation of a theorem of Birch on the distribution of rational point counts for elliptic curves with prescribed 2-torsion over a fixed finite field.
| Type: | Article |
|---|---|
| Title: | Traces of hecke operators and refined weight enumerators of reed-solomon codes |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/tran/7089 |
| Publisher version: | https://doi.org/10.1090/tran/7089 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10084825 |
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