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How to enhance hamming code with quadratic residue?

Quadratic residue

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To enhance Hamming codes with quadratic residue, one can consider a generalization of quadratic residue codes to higher power residues, which can improve information transmission rates compared to traditional quadratic residue codes. Another approach involves lattice-quantizing data points using an Extended Hamming Code, correcting errors, and transforming the initial codeword into an extended quadratic residue form for transmission and recovery. Additionally, utilizing the Residue Number System (RNS) can convert large decimal numbers into smaller groups, simplifying computations and reducing resource usage. Explicit expressions of generating idempotents for higher power residue codes over binary fields can also be computed to enhance Hamming codes with quadratic residue properties. By leveraging these methods, one can enhance Hamming codes with the advantages and efficiencies offered by quadratic residue techniques.

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Open access•Proceedings Article•DOI Generating Idempotents of Residue Codes over The Binary Field Dong Xuedong, Zhang Yan - Show less +1 more 01 Jan 2017 2 Citations	Generating idempotents of residue codes over the binary field can enhance Hamming codes with quadratic residue properties, improving code rates and minimum distances.
Patent Method for storage and reconstruction of the extended hamming code for an 8-dimensional lattice quantizer Michael Samuel Postol 09 Jul 1999 69 Citations	The method enhances Hamming code by transforming the initial codeword into an extended quadratic residue form, improving error correction capabilities in an 8-dimensional lattice quantizer.
Journal Article•DOI A generalisation of quadratic residue codes to the case of cubic and biquadratic residues D. N. Semyonovykh 01 Nov 2005-Discrete Mathematics and Applications 1 Citations	Generalize quadratic residue codes to cubic and biquadratic residues to enhance the information transmission rate, sacrificing code distance, by constructing generating polynomials for higher power residues.
Proceedings Article•DOI Implementation of Hamming coding in Residue Number System B. Raghavaiah, Omprakash - Show less +1 more 01 Mar 2018 1 Citations	Not addressed in the paper.

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