Abstract
Reed–Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where the length is static, the appropriate length can be obtained from an RS code by shortening or puncturing. Generalized Reed–Solomon (GRS) codes are a generalization of RS codes, whose subfield-subcodes (SFSC) are extensively studied. In this paper we show that a particular class of GRS codes produces many SFSC with large dimension. We present two algorithms for searching through these codes and a list of new best-known codes obtained.
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