\mathbbF_q\mathbbF_q²-additive cyclic codes and their Gray images

2025/11/04 by Ankit Yadav, Yadav, Ankit, Ritumoni Sarma +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2511.02325

openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

Abstract

We investigate additive cyclic codes over the alphabet \mathbbF_q\mathbbF_q², where q is a prime power. First, its generator polynomials and minimal spanning set are determined. Then, examples of \mathbbF_q²-additive cyclic codes that satisfy the well-known Singleton bound are constructed. Using a Gray map, we produce certain optimal linear codes over \mathbbF₃. Finally, we obtain a few optimal ternary linear complementary dual (LCD) codes from \mathbbF₃\mathbbF₉-additive codes.

Citations

• Nonbinary quantum codes
• Construction of Additive Complementary Dual Codes Over Finite Fields

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