On the Feng-Rao Bound for the L -construction of Algebraic Geometry Codes
Ryutaroh Matsumoto, Shinji Miura · 2000
which is called the L-construction, was not explicitly mentioned by Goppa but known to researchers including Goppa and Manin [17, p.386]. CL(D,mQ) seems to be first explicitly defined in [8], [15]. Most research articles treat only CΩ(D,mQ). A reason for this trend may be due to the lack of efficient decoding algorithms for CL(D,mQ), while we know efficient decoding algorithms for CΩ(D,mQ) proposed by Feng and Rao [1] and Sakata et al. [12]. In this paper we show how to apply the Feng-Rao algorithm to CL(D,mQ). The reader may wonder if there is any advantage considering CL(D,mQ) over CΩ(D,mQ). We shall give examples in which the error-correcting capability of CL(D,mQ) is larger than CΩ(D,mQ) while their dimensions are the same, where F,D,Q are common to CL(D,mQ) and CΩ(D,mQ). Thus it is worth considering CL(D,mQ) as well for fixed F,D,Q.