New Instances of Quantum Error-Correcting Codes for Single Deletion Errors

This paper provides new instances of quantum error-correcting codes. According to recent results by Nakayama and Hagiwara, by using two sets of binary sequences that satisfy three conditions, we can construct quantum error-correcting codes for single deletion errors. However, only two instances of two sets that satisfy the three conditions have been found to date. The present study constructs two infinite series of sets that satisfy the three conditions. In other words, this paper constructs new infinite series of quantum error-correcting codes for single deletion errors.