Binary and ternary LCD codes from projective spaces

We construct binary and ternary Linear Complementary Dual (LCD) codes with parameters [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text]. Further, we derive and study properties of a class of two, three and four weight codes [Formula: see text]. We show that under suitable conditions [Formula: see text] codes are self-orthogonal and satisfy the Griesmer bound.

On the Minimum Length of Linear Codes over the Field of 9 Elements

We construct a lot of new $[n,4,d]_9$ codes whose lengths are close to the Griesmer bound and prove the nonexistence of some linear codes attaining the Griesmer bound using some geometric techniques through projective geometries to determine the exact value of $n_9(4,d)$ or to improve the known bound on $n_9(4,d)$ for given values of $d$, where $n_q(k,d)$ is the minimum length $n$ for which an $[n,k,d]_q$ code exists. We also give the updated table for $n_9(4,d)$ for all $d$ except some known cases.