How to Expand a Self-orthogonal Code

Jon-Lark Kim; Hongwei Liu; Jinquan Luo

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arXiv · 2511.17503

How to Expand a Self-orthogonal Code

Jon-Lark Kim·Hongwei Liu·Jinquan Luo

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Abstract

In this paper, we show how to expand Euclidean/Hermitian self-orthogonal code preserving their orthogonal property. Our results show that every $k$-dimension Hermitian self-orthogonal code is contained in a $(k+1)$-dimensional Hermitian self-orthogonal code. Also, for $k< n/2-1$, every $[n,k]$ Euclidean self-orthogonal code is contained in an $[n,k+1]$ Euclidean self-orthogonal code. Moreover, for $k=n/2-1$ and $p=2$, we can also fulfill the expanding process. But for $k=n/2-1$ and $p$ odd prime, the expanding process can be fulfilled if and only if an extra condition must be satisfied. We also propose two feasible algorithms on these expanding procedures.

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Jon-Lark Kim, Hongwei Liu, Jinquan Luo. 2025-07-30. How to Expand a Self-orthogonal Code. https://arxiv.org/abs/2511.17503

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