# Construction of Additive Complementary Dual Codes Over Finite Fields

Source: [Construction of Additive Complementary Dual Codes Over Finite Fields](<https://www.sota2.com/research/paper/68fa5e791e209131ce9e293c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T10:33:27.964Z

Authors: Gyanendra K. Verma, R. K. Sharma

Published: 2023-02-23T06:12:14.000Z

## Abstract

In this work, we investigate additive complementary dual (ACD) codes and their construction over finite fields $\\mathbb{F}\_{q^2}$ with respect to the trace inner products, where $q$ is a prime power. First, we associate an additive code with a matrix known as a generator matrix. After that, we describe ACD codes in terms of generator matrices for the trace Hermitian and the trace Euclidean inner products. We also construct ACD codes over $\\mathbb{F}\_{q^2}$ from linear codes over $\\mathbb{F}\_q.$ Additionally, we present techniques for constructing ACD codes with various parameters from a given ACD code over $\\mathbb{F}\_{q^2}.$ By applying these methods, we construct numbers of trace Euclidean and trace Hermitian ACD codes that exhibit better parameters compared to the best known linear codes over $\\mathbb{F}\_9$ and $\\mathbb{F}\_4$ of the same size and length.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2302.11791>)

[PDF](<https://arxiv.org/pdf/2302.11791.pdf>)