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These properties serve as the foundation for comprehending the distinctive characteristics that [Formula: see text]-spectral codes offer, ensuring the integrity and reliability of transmitted data. Our exploration extends to the construction of maximum distance separable (MDS) [Formula: see text]-spectral codes, which boast the maximum error correction capability. As a culmination of our research, we present an efficient decoding technique tailored for [Formula: see text]-spectral codes. Leveraging an MDS [Formula: see text]-spectral code and our decoding technique, we achieve optimal error correction and ensure good numerical stability. This innovative approach opens new avenues for enhancing the performance of real-number codes in practical applications. <\/jats:p>","DOI":"10.1142\/s1793830924500551","type":"journal-article","created":{"date-parts":[[2024,5,30]],"date-time":"2024-05-30T16:07:29Z","timestamp":1717085249000},"source":"Crossref","is-referenced-by-count":1,"title":["Spectral codes of real symmetric operators for error correction"],"prefix":"10.1142","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7847-5597","authenticated-orcid":false,"given":"N.","family":"Suresh Babu","sequence":"first","affiliation":[{"name":"Department of Mathematics, University College, University of Kerala, Thiruvananthapuram 695034, Kerala, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1257-7558","authenticated-orcid":false,"given":"B.","family":"Ravivarma","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University College, University of Kerala, Thiruvananthapuram 695034, Kerala, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0894-8472","authenticated-orcid":false,"given":"E. 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