A class of error-detecting codes based on T-quasigroups

In this paper, we propose a new class of error-detecting codes based on quasigroups using automorphisms of the finite field [Formula: see text] and the additive group [Formula: see text]. We demonstrate that these codes are effective in detecting burst errors caused by hardware damage or noisy transmission. We also explore the codes ability to detect various types of double errors, including transposition errors, twin errors, and phonetic errors. Our analysis extends beyond bit-level errors to include block-level errors. Finally, we provide a comparative analysis and demonstrate the real-world applications of our code.