Published April 30, 2026
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An MDS Code Generated from a Three-Term Exponential Sum
Authors/Creators
- 1. Assistant Professor, Department of Mathematics, Central University of Jharkhand Building, Ranchi (Jharkhand), India.
Description
Abstract: In this paper, I investigate the method for constructing Maximum Distance Separable (MDS) codes using exponential sums. By utilizing the properties of the trace function over finite fields, I explicitly calculate linear codes associated with certain three-term exponential sums. The parameters, weight distributions, and distance properties of these codes are analyzed in detail. Furthermore, we analyse the syndrome-decoding process for these codes.
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Additional details
Identifiers
- DOI
- 10.54105/ijam.A1241.06010426
- EISSN
- 2582-8932
Dates
- Accepted
-
2026-04-15Manuscript received on 28 February 2026 | First Revised Manuscript received on 10 March 2026 | Second Revised Manuscript received on 25 March 2026 | Manuscript Accepted on 15 April 2026 | Manuscript published on 30 April 2026.
References
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- G.Jain, Z.Lin, R.Fena, "Two Weight and Three Weight Linear Codes Based on Weil Sums", Finite Fields and Their Applications. 57, 92-107 (2019). DOI: https://doi.org/10.1016/j.ff9.2019.02.001
- Zhao Hu,Nian Li, Xi. Zeng, "New linear codes with few weights derived from Kloostermann sum", Finite Fields and their Application. 62,101608 (2020). DOI: https://doi.org/10.1016/j.ffa.2019.101608