Linear codes with complementary duals (LCD) are linear codes whose intersection with their dual are trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault injection attacks. Nonbinary LCD codes in characteristic 2 can be transformed into binary LCD codes by expansion. In this paper, we introduce a general construction of LCD codes from any linear codes. Further, we show that any linear code over F _q (q > 3) is equivalent to a Euclidean LCD code and any linear code over F _q ² (q > 2) is equivalent to a Hermitian LCD code. Consequently an [n, k, d]-linear Euclidean LCD code over F _q with q > 3 exists if there is an [n, k, d]-linear code over F _q and an [n, k, d]-linear Hermitian LCD code over F _q ² with q > 2 exists if there is an [n, k, d]-linear code over F _q ² . Hence, when q > 3 (resp. q > 2) q-ary Euclidean (resp. q ² -ary Hermitian) LCD codes possess the same asymptotical bound as q-ary linear codes (resp. q ² -ary linear codes). This gives a direct proof that every triple of parameters [n, k, d] which is attainable by linear codes over F _q with q > 3 (resp. over F _q ² with q > 2) is attainable by Euclidean LCD codes (resp. by Hermitian LCD codes). In particular there exist families of q-ary Euclidean LCD codes (q > 3) and q ² -ary Hermitian LCD codes (q > 2) exceeding the asymptotical Gilbert-Varshamov bound. Further, we give a second proof of these results using the theory of Gröbner bases. Finally, we present a new approach of constructing LCD codes by extending linear codes.

Minimal linear codes have significant applications in secret sharing schemes and secure twoparty computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many construction methods for linear codes from functions have been proposed in the literature. In this paper, we generalize the recent construction methods given by Tang et al. in IEEE Transactions on Information Theory, 62(3), 1166-1176, 2016 to weakly regular plateaued functions over finite fields of odd characteristic. We first construct threeweight linear codes from weakly regular plateaued functions based on the second generic construction and then determine their weight distributions. We also give a punctured version and subcode of each constructed code. We note that they may be (almost) optimal codes and can be directly employed to obtain (democratic) secret sharing schemes, which have diverse applications in the industry. We next observe that the constructed codes are minimal for almost all cases and finally describe the access structures of the secret sharing schemes based on their dual codes.

Linear complementary dual (LCD) cyclic codes were referred historically to as reversible cyclic codes, which had applications in data storage. Due to a newly discovered application in cryptography, there has been renewed interest in LCD codes. In particular, it has been shown that binary LCD codes play an important role in implementations against side-channel attacks and fault injection attacks. In this paper, we first present a new characterization of binary LCD codes in terms of their orthogonal or symplectic basis. Using such a characterization, we solve a conjecture proposed by Galvez et al. on the minimum distance of binary LCD codes. Next, we consider the action of the orthogonal group on the set of all LCD codes, determine all possible orbits of this action, derive simple closed formulas of the size of the orbits, and present some asymptotic results on the size of the corresponding orbits. Our results show that almost all binary LCD codes are odd-like codes with odd-like duals, and about half of q-ary LCD codes have orthonormal basis, where q is a power of an odd prime.