Abstract
In this paper, a construction of one-point Klein codes over finite field (Formula presented.) with (Formula presented.) 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 (Formula presented.) 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. © 2013, Springer Science+Business Media New York.