Further Study of p-Ary Self-Orthogonal Codes From Square Functions
Abstract
In this paper, we investigate a family of trace codes over finite fields of odd characteristic defined by two quadratic trace conditions. By analyzing the quadratic forms associated with these trace conditions and evaluating the corresponding character sums, we obtain the parameters and complete weight distributions of the codes. We further exploit the natural multiplicative orbit structure of the defining sets to obtain punctured codes and determine their parameters, weight distributions and dual distances. Moreover, we establish self?orthogonality criteria and investigate divisibility and projectivity of the constructed codes. These results give a unified treatment for arbitrary odd prime fields and for extension degrees of both parities.
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BibTeX
@misc{wu2026further,
title = {{Further Study of p-Ary Self-Orthogonal Codes From Square Functions}},
author = {Tingting Wu and Xianhong Xie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35346},
eprint = {2610.35346},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35346},
}
RIS
TY - UNPB
TI - Further Study of p-Ary Self-Orthogonal Codes From Square Functions
AU - Tingting Wu
AU - Xianhong Xie
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35346
UR - https://arxiv.org/abs/2610.35346
AB - In this paper, we investigate a family of trace codes over finite fields of odd characteristic defined by two quadratic trace conditions. By analyzing the quadratic forms associated with these trace conditions and evaluating the corresponding character sums, we obtain the parameters and complete weight distributions of the codes. We further exploit the natural multiplicative orbit structure of the defining sets to obtain punctured codes and determine their parameters, weight distributions and dual distances. Moreover, we establish self?orthogonality criteria and investigate divisibility and projectivity of the constructed codes. These results give a unified treatment for arbitrary odd prime fields and for extension degrees of both parities.
ER -