One-point Klein codes and their serial-in-serial-out systematic encoding

Abstract

In this paper, a construction of one-point Klein codes over finite field $F_q$ with $q$ a prime power is illustrated. A lot more good one-point Klein codes can be found than good three-point Klein codes in the literature. Many one-point Klein codes over $F_q$ are near-MDS long codes. Instead of using automorphisms to facilitate the decoding of the Klein codes, automorphisms are used to derive a systematic encoding for the Klein codes via Gröbner bases. This systematic encoding promises an efficient serial-in-serial-out hardware architecture for the encoder with considerably less complexity than the brute-force one.