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cyclic_code.md

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Cyclic Codes

Cyclic codes are a subtype of LinearCode and inherit its methods. For more information on how to use these functions, see the cyclic code tutorial.

Cyclotomic Cosets

The following set of functions are useful for defining cyclic codes.

ord
cyclotomic_coset
all_cyclotomic_cosets
complement_qcosets
qcoset_pairings
qcoset_table
dual_qcosets

Constructors

CyclicCode
BCHCode
ReedSolomonCode
QuadraticResidueCode

Attributes

splitting_field
polynomial_ring
primitive_root
offset
design_distance
qcosets
qcosets_reps
defining_set
zeros
nonzeros
generator_polynomial
parity_check_polynomial
idempotent
BCH_bound
is_narrowsense
is_reversible
CodingTheory.is_degenerate
is_primitive
is_antiprimitive

Methods

defining_set
dual_defining_set
CodingTheory.is_cyclic
complement
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