It is well known that linear block codes can achieve capacity and hence study of good codes can be limited to study of linear block codes. It is also well known that BCH codes are asymptotically bad and cannot achieve capacity. What are the corresponding results for cyclic codes that fall between these two classes of codes? Can they achieve capacity? Can they achieve the cutoff rate? Is their error exponent different from linear block codes?
2026-03-31 22:20:35.1774995635
Are cyclic codes good?
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