Shortened Linear Codes Over Finite Fields

The puncturing and shortening techniques are two important approaches to constructing new linear codes from old ones. In the past 70 years, a lot of progress on technique has been made, many works punctured have done. Many families with interesting parameters obtained technique. However, little research done there only handful references shortened codes. first objective this paper is prove some general theory for second study Hamming codes, Simplex Reed-Muller ovoid Eleven optimal over finite fields presented in paper. As byproduct, five infinite 2-designs also constructed