Quadratic residue codes over Z₄₉

Key Points

• The aim is to examine quadratic residue codes defined over the integers modulo 49, focusing on their properties and decoding capabilities.
• Investigated the structure of quadratic residue codes for prime lengths over Z49.
• Defined codes using generating idempotents and studied their extended versions.
• Analyzed the automorphism groups of these codes.
• Extended quadratic residue codes over Z49 were shown to have large automorphism groups.
• The properties of these groups can enhance decoding efficiency for quadratic residue codes.