Optimal Linear Codes Over the Field of Order 7 - Nomura, Keita; Maruta, Tatsuya (2020 Algebraic and Combinatorial Coding Theory (ACCT), 2020)
We construct some new linear codes over the field of order 7 to determine the exact value of the minimum length for which a linear code of dimension four with given minimum weight exists for some open cases. Most of the new codes are constructed as projective duals of some 7-divisible codes from some orbits of a projectivity in the projective space.