Decoding of Dual-Containing Codes From Hermitian Tower and Applications

In this paper, we study the decoding of dual-containing codes from Hermitian tower and applications to quantum codes. The contribution of this paper is threefold. First, we construct the quantum stabilizer codes from the Hermitian tower. Second, we provide a deterministic decoding algorithm with decoding radius that almost achieves the optimal decoding radius, i.e., (1-R)/4 , where R is the rate. Last and most importantly, we present a Monte Carlo algorithm with decoding radius roughly equal to (1-R)/3 , which is beyond the optimal decoding radius (1-R)/4 . There are several features in this paper. First of all, we employ a differential for the Hermitian tower. This differential plays a crucial role for decoding. We also extend our decoding by passing to the constant field extension. This constant field extension makes the decoding work perfectly.