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arXiv · 2412.09915

On the Structure of Two-Dimensional Constacyclic Codes using Common Zero Sets

Vidya Sagar·Shikha Patel·Ashutosh Singh·Shayan Srinivasa Garani
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Abstract

We consider two-dimensional $(\lambda_1, \lambda_2)$-constacyclic codes over $\mathbb{F}_{q}$ of area $M N$, where $q$ is some power of prime $p$ with $\gcd(M,p)=1$ and $\gcd(N,p)=1$. With the help of common zero (CZ) set, we characterize 2-D constacyclic codes. Further, we provide an algorithm to construct an ideal basis of these codes by using their essential common zero (ECZ) sets. We also describe the dual of 2-D constacyclic codes. Finally, we provide an encoding scheme for generating 2-D constacyclic codes from the generator tensor, implementable in a parallel fashion. Through examples, we illustrate that 2-D constacyclic codes can have better minimum distance compared to their cyclic counterparts with the same code area and code rate, generalizing prior work over 2-D binary cyclic coded arrays.

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Vidya Sagar, Shikha Patel, Ashutosh Singh, Shayan Srinivasa Garani. 2024-12-13. On the Structure of Two-Dimensional Constacyclic Codes using Common Zero Sets. https://arxiv.org/abs/2412.09915

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