One-point Klein codes and their serial-in-serial-out systematic encoding
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 Grbner 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.
klein codes systematic encoding grbner bases algebraic-geometry codes error-correcting codes 94b05