Abstract
Linear codes with complementary-duals (LCD) have many applications in cryptography, communication systems and data storage. A q-ary linear code C is called LCD if C∩C⊥ = {0} holds. Using method of coset theory, we deduce a characterization of LCD cyclic code by its defining set. Then two families of q-ary MDS cyclic LCD codes with lengthes n| (q+1) and n| (q-1) are determined and many new classes of LCD MDS codes are gained.
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