Error Correction for Check Digit Systems over p-Groups and Applications to DNA Sequences

Abstract

Statistical analysis shows that the most common errors in the transmission of information consist of single errors and transposition errors. Error detection and correction methods are often desired, particularly when the accuracy of information is of crucial importance. Inspired by a check digit system constructed from the companion matrix of a primitive polynomial over the integers Zp and that focused on error detection, this work develops error-correction formulas for single errors and transposition errors for that check digit scheme. We also propose an application to DNA sequences.

Keywords

• error correction
• check digit
• companion matrix
• Galois field