On weight distribution of a class of subfield codes of hyperoval codes

Abstract

Abstract: Let F_q be a finite field of cardinality q, q=2^mand m>1.Assuming that h is a positive integer and coprime with m, for the translation o-polynomial $f(x)=x^{2^{h}}$, let $C_{H(f)}^{(2)}$ be the binary subfield codes of the hyperoval code C_H(f). Based on the trace function representation of $C_{H(f)}^{(2)}$ and the theory of exponential sums over finite fields, the weight distribution of $C_{H(f)}^{(2)}$ is obtained. The parameters of $C_{H(f)}^{(2)}$ and its dual code $C_{H(f)}^{(2)\perp}$ are determined.

Key words: linear code, hyperoval code, subfield code, weight distribution

CLC Number:

CHENG Wei-dong, CHENG Wen-hao. On weight distribution of a class of subfield codes of hyperoval codes[J]. Journal of Lanzhou University of Technology, 2025, 51(5): 167-172.

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