An MDS Code Generated from a Three-Term Exponential Sum
Shikha Singh
Dr. Shikha Singh, Assistant Professor, Department of Mathematics, Central University of Jharkhand Building, Ranchi (Jharkhand), India.
Manuscript 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 | PP: 57-61 | Volume-6 Issue-1, April 2026 | Retrieval Number: 100.1/ijam.A124106010426 | DOI: 10.54105/ijam.A1241.06010426
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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.
Keywords: Three-Term Exponential Sum, Linear Code, Syndrome Decoding, MDS Code. MSC: 11 LO5.
Scope of the Article: Number Theory