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A novel coding scheme for generating sixteen codes from quaternary codes with applications

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Abstract

Digital data transmission and storage are indispensable components for our contemporary information-driven society. As data volumes keep increasing, the need for efficient coding schemes grows. This paper gives a novel coding scheme for generating sixteen codes from generators with quaternary codes, thereby offering a significant increase in data representation capacity, new possibilities for data encoding and decoding, and an overall improvement in the efficiency of the encoding scheme. This provides up a new perspective for numerous fields that can profit from the proposed scheme, including coding theory, computer science, modeling, and experimental design. We focus on only experimental design and modeling, due to space limits and their importance in designing and modeling real-world and scientific phenomena. The main findings indicate that the new generated sixteen codes can be used as optimal experimental designs with good space-filling behavior when designing large-scale experiments, and as efficient datasets that perform well in fitting various functions even with a small number of points and without modeling assumptions. The relationships between the codewords of the generated sixteen codes and the codewords of the generator quaternary codes are investigated. These relationships provide a benchmark by which to select the generator most efficiently, resulting in codewords that are efficient from multiple angles. Furthermore, the space-filling behavior and isomorphism examination of the sixteen codes generated as designs are deeply theoretically studied.

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Acknowledgements

The author greatly appreciate valuable comments and suggestions of the referees and Editor that significantly improved the paper. Elsawah greatly appreciates the kind support of Prof. Kai-Tai Fang.

Funding

This work was supported by the UIC Research Grants with no. of (R201912 and R202010); the Curriculum Development and Teaching Enhancement with no. of (UICR0400046-21CTL); the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College with no. of (2022B1212010006); and the Guangdong Higher Education Upgrading Plan (2021–2025) with no. of (UIC R0400001-22).

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Authors and Affiliations

  1. Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, Beijing Normal University-Hong Kong Baptist University United International College, Zhuhai, 519087, China

    A. M. Elsawah

  2. Department of Statistics and Data Science, Faculty of Science and Technology, Beijing Normal University-Hong Kong Baptist University United International College, Zhuhai, 519087, China

    A. M. Elsawah

  3. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt

    A. M. Elsawah

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  1. A. M. Elsawah
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Correspondence to A. M. Elsawah.

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Communicated by Vinicius Albani.

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Elsawah, A.M. A novel coding scheme for generating sixteen codes from quaternary codes with applications. Comp. Appl. Math. 43, 118 (2024). https://doi.org/10.1007/s40314-024-02596-8

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