High-Dimensional Cross Parity Codes and Parities from Lower Than (d − 1)-Dimensional Hyperplanes - Jörg Keller (Computers)
Cross parity codes are mostly used as 2-dimensional codes, and sometimes as 3-dimensional codes. We argue that higher dimensions can help to reduce the number of parity bits, and thus deserve further investigation. As a start, we investigate parities from <semantics>(d−2)</semantics>-dimensional hyperplanes in d-dimensional parity codes, instead of parities from <semantics>(d−1)</semantics>-dimensional hyperplanes as usual.