Linear codes with covering radius 3
The shortest possible length of a q-ary linear code of covering radius R and codimension r is called the length function and is denoted by a"" (q) (r, R). Constructions of codes with covering radius 3 are here developed, which improve best known upper bounds on a"" (q) (r, 3). General constructions are given and upper bounds on a"" (q) (r, 3) for q = 3, 4, 5, 7 and r a parts per thousand currency sign 24 are tabulated.
covering radius concatenation projective geometry saturating set