Construction of Minimal Binary Linear Codes of dimension $n+3$

Wajid M. Shaikh; Rupali S. Jain; B. Surendranath Reddy; Bhagyashri S. Patil

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arXiv · 2403.13350

Construction of Minimal Binary Linear Codes of dimension $n+3$

Wajid M. Shaikh·Rupali S. Jain·B. Surendranath Reddy·Bhagyashri S. Patil

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Abstract

In this paper, we will give the generic construction of a binary linear code of dimension $n+3$ and derive the necessary and sufficient conditions for the constructed code to be minimal. Using generic construction, a new family of minimal binary linear code will be constructed from a special class of Boolean functions violating the Ashikhmin-Barg condition. We also obtain the weight distribution of the constructed minimal binary linear code.

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Wajid M. Shaikh, Rupali S. Jain, B. Surendranath Reddy, Bhagyashri S. Patil. 2024-03-20. Construction of Minimal Binary Linear Codes of dimension $n+3$. https://arxiv.org/abs/2403.13350

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