SOME SHORTENED CODES FROM LINEAR CODES CONSTRUCTED BY DEFINING SETS

The puncturing and shortening technologies are two important approaches to construct new linear codes. It is noticed that many works on punctured linear codes have been done in the past few decades, but till now little research on the shortening technique has been done and there are only a handful references on shortened linear codes. In this paper, we use the shortening technology to obtain some shortened codes from linear codes constructed by certain special defining sets, and explicitly determine their parameters. Some of those shortened codes are optimal or almost optimal.