Two families of self-orthogonal codes with applications in LCD codes and optimally extendable codes

Self-orthogonal codes have interesting applications in quantum codes, linear complementary dual (LCD) codes and lattices. LCD codes and (almost) optimally extendable codes are useful to safeguard against Side-Channel Attacks (SCAs) and Fault Injection Attacks (FIAs). In this paper, we first give a lower bound of dual distances for augmented codes via the defining-set construction. Then we construct two families of q -ary self-orthogonal codes with determined weight distributions via defining-set construction and propose the parameters of their duals. Besides, several families of AMDS codes are obtained as byproducts, which are both length-optimal and dimension-optimal with respect to the Sphere-packing bound. As applications, these self-orthogonal codes are used to construct LCD codes and proved to be optimally extendable. As a consequence, our constructions produce some optimal codes.