On the structure of Hermitian codes and decoding for burst errors

In this paper, we first prove that every Hermitian code is a direct sum of concatenated Reed-Solomon codes over GF(q²), which provides a new method to calculate the dimension of the Hermitian code. Based on this, we present a new decoding algorithm for Hermitian code. Our algorithm is especially efficient in decoding burst errors. Finally, a method to optimize Hermitian code is obtained. The optimized code maintains the same dimension and error correctability, but the complexity for burst error correction can be reduced from O(n⁵3/) to O(n).