On generalized hyperbolic cascaded Reed-Solomon codes

Abstract

In this paper, a generalized version of the Hyperbolic Cascaded Reed–Solomon (HCRS) code proposed by K. Saints and C. Heegard is considered. The lower bound of the minimum distance (the design distance) is investigated. This is a linear code that can be expressed as (n, k, d min = d ) on GF(q). Here, n, k, dmin, and d are the code length, dimension, minimum distance, and design distance, respectively. The proposed code has more degrees of freedom in selection of the code length than the HCRS code. Codes with various code length can be constructed easily. However, in the m-dimensional space on GF(q), the selectable code length is less than qm. When the proposed code with a code length less than qm is compared with the shortened code with the same code length obtained by shortening the m-dimensional HCRS code with a code length of qm [or (q−1)m], the design distances are identical, whereas the proposed code has an equal or greater dimension compared with the HCRS code. Also, from the proposed code, it is relatively easy to construct a code of the same code length as the algebraic geometric code (geometric Goppa code) and the improved geometric Goppa code proposed by Feng and Rao. Further, when the performance (parameters) is compared at a high coding rate (k/n), the proposed code sometimes has equal or better performance. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(11): 18–27, 1999