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A [Formula: see text]-ary linear code [Formula: see text] is called a linear complementary dual (LCD) code if it meets its dual trivially. Binary LCD codes play a significant role for their advantage of low complexity for implementations against side-channel attacks and fault injection attacks. In this paper, the problem of finding LCD codes over the binary field is discussed. Many new codes and new bounds are presented, as well as a table of optimal LCD codes (or upper and lower bounds on such codes) of length up to 30 bits.

The entanglement-assisted (EA) formalism allows arbitrary classical linear codes to transform into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this work, we propose a decomposition of the defining set of constacyclic codes. Using this method, we construct four classes of q-ary entanglement-assisted quantum MDS (EAQMDS) codes based on classical constacyclic MDS codes by exploiting less pre-shared maximally entangled states. We show that a class of q-ary EAQMDS have minimum distance upper limit greater than 3q − 1. Some of them have much larger minimum distance than the known quantum MDS (QMDS) codes of the same length. Most of these q-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.

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