Speaker
Description
In this talk, we present a family of algebraically constructed hierarchical quasi-cyclic codes. These codes are built from Reed-Solomon and polynomial evaluation codes using a construction of superimposed codes by Kautz and Singleton. Using a novel ordering of the codewords and evaluation points, we show both the number of levels in the hierarchy and the index of these $q$-ary-derived codes are determined by the field size. We compute explicit code parameters and properties as well as some additional bounds on parameters such as rank and distance. In particular, starting with Reed-Solomon codes of dimension two yields hierarchical quasi-cyclic codes with Tanner graphs of girth 6. Finally, we present a table of small code parameters and note that some of these codes meet the best known minimum distance for binary codes, with the additional hierarchical quasi-cyclic structure.