2023/05/31 by Chunlei Liu, Liu, Chunlei
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2305.19565
openalex publication_date 2023/05/31 · openalex created_date 2023/06/02 · openalex updated_date 2026/07/28
On a Goppa code whose structure polynomial has coefficients in the symbol field, the Frobenius acts. Its fixed codewords form a subcode. Deleting the naturally occurred redundance, we obtain a new code. It is proved that these new codes approach the Gilbert-Varshamov bound. It is also proved that these codes can be decoded within O(n2(\logn)a) operations in the symbol field, which is usually much small than the location field, where n is the codeword length, and a a constant determined by the polynomial factorization algorithm.