Burst error-correcting quantum stabilizer codes designed from idempotents

Abstract Certain classical codes can be viewed isomorphically as ideals of group algebras, while studying their algebraic structures help extracting the code properties. Research has shown that this was remarkably efficient in case when generators are idempotents. In quantum error correction, theory stabilizer formalism requires self-orthogonal additive over finite field GF (4), which, via lens essentially $$F_2$$ F 2 -submodules (4). Therefore, paper provides a classification on idempotents commutative algebra (4) G , followed by criterion allows to generate subgroups. Later, construction is done cyclic $$C_n$$ C n for $$n=2^m-1$$ = m - 1 and $$n=2^m+1$$ + . Quantum bounds burst minimum distance subsequently determined.