Fault-tolerant quantum computation with simple non-LDPC high-rate codes

I study a family of non-LDPC high-rate codes toward low-overhead fault-tolerant quantum computation. The coding rates of the codes studied in this work are higher than or as high as 20%. I develop a high-performance decoder dedicated to these codes. Exploiting the simple structure of the code family, I also propose fault-tolerant methods for logical Clifford and non-Clifford gates allowing simultaneous execution.