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Creators/Authors contains: "Korchmáros, Gábor"

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  1. ; ; ; ; (, Designs, Codes and Cryptography)
    Abstract Datta and Johnsen (Des Codes Cryptogr 91:747–761, 2023) introduced a new family of evaluation codes in an affine space of dimension$$\ge 2$$ ≥ 2 over a finite field$${\mathbb {F}}_q$$ F q where linear combinations of elementary symmetric polynomials are evaluated on the set of all points with pairwise distinct coordinates. In this paper, we propose a generalization by taking low dimensional linear systems of symmetric polynomials. Computation for small values of$$q=7,9$$ q = 7 , 9 shows that carefully chosen generalized Datta–Johnsen codes$$\left[ \frac{1}{2}q(q-1),3,d\right] $$ 1 2 q ( q - 1 ) , 3 , d have minimum distancedequal to the optimal value minus 1. 
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    Free, publicly-accessible full text available May 12, 2026