On LCD codes over Z 4

Abstract

Linear complementary dual(LCD) codes are being utilized to protect cryptographic implementations from side-channel and fault attacks. In this work, LCD codes over the ring Z 4 are examined. It is observed that an LCD cyclic code over Z 4 of odd length is always reversible. However, the converse of this result does not hold. A suitable example to validate this statement is presented. Further, a necessary and sufficient condition for a reversible cyclic code of odd length to be an LCD code is obtained. Finally, it is found that among cyclic codes of length 2 k , no non-trivial LCD code exists.