High-dimensional symmetric interleaved parity check code-general high-dimensional ring code

A new n-dimensional symmetric parity check code, named the ring code, is proposed. The code is constituted by means of the product space of cyclic-shifted versions of one-dimensional parity check codes, which shows crystalline structural symmetries. The ring code which is based on a two-dimensional ring code has a symmetrical structure. An n-dimensional ring code can easily be formed with (n-l)-dimensional ring codes. The reason why the authors propose this code is the high capacity of correcting burst errors, random errors and multi-burst errors for high-dimensional case. They propose the formation of a general n-dimensional symmetric ring code and show the features and performance of the high-dimensional ring code