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Coding Theory Documentation
  • Introduction
  • Tutorials
    • Linear Codes Over Finite Fields
    • Cyclic Codes
    • Quantum Codes
    • Weight Reduction
  • Examples
    • The Vardy-Be’ery Decomposition
    • Quantum Reed-Muller Codes
  • Classical
    • Linear Codes
    • Concatenated Codes
    • Cyclic Codes
    • Quasi-Cyclic Codes
    • Generalized Reed-Solomon Codes
    • Reed-Muller Codes
    • Modifying Codes
    • Product Codes
    • Miscellaneous Known Linear Codes
  • LDPC
    • LDPC Codes
    • Generalized LDPC/Tanner Codes
    • LDPC Ensemble Analysis
    • LDPC Noise Channels
    • Decoding LDPC Codes
  • Quantum
    • Notes
    • Product Codes
    • Miscellaneous Known Stabilizer Codes
    • Weight Reduction
  • Misc
    • Tilings
    • Trellises
    • Utilies
    • Weight Enumerators, Distributions, And Minimum Distances
  • References
  • Index
Version
  • Index
  • Index
Edit on GitHub
  • CodingTheory.BAWGNChannel
  • CodingTheory.BCHCode
  • CodingTheory.BinaryErasureChannel
  • CodingTheory.BinarySymmetricChannel
  • CodingTheory.CyclicCode
  • CodingTheory.GeneralizedReedSolomonCode
  • CodingTheory.LDPCCode
  • CodingTheory.LinearCode
  • CodingTheory.MatrixProductCode
  • CodingTheory.QuasiCyclicCode
  • CodingTheory.ReedMullerCode
  • CodingTheory.ReedSolomonCode
  • AbstractAlgebra.VectorSpace
  • AbstractAlgebra.lift
  • AbstractAlgebra.lift
  • AbstractAlgebra.polynomial
  • AbstractAlgebra.polynomial_ring
  • Base.:+
  • Base.:∩
  • Base.:⊆
  • Base.copy
  • Base.in
  • Base.length
  • Base.zeros
  • CodingTheory.:⊕
  • CodingTheory.ACE_distribution
  • CodingTheory.ACE_spectrum
  • CodingTheory.CWE_to_HWE
  • CodingTheory.ExtendedGolayCode
  • CodingTheory.GolayCode
  • CodingTheory.HammingCode
  • CodingTheory.Hamming_distance
  • CodingTheory.Hamming_weight
  • CodingTheory.Hermitian_conjugate_matrix
  • CodingTheory.Hermitian_dual
  • CodingTheory.Hermitian_hull
  • CodingTheory.Hermitian_inner_product
  • CodingTheory.Hexacode
  • CodingTheory.LP_decoder_LDPC
  • CodingTheory.QDistRndCSS
  • CodingTheory.QuadraticResidueCode
  • CodingTheory.RepetitionCode
  • CodingTheory.SimplexCode
  • CodingTheory.Singleton_bound
  • CodingTheory.Sterns_attack
  • CodingTheory.Tanner_code
  • CodingTheory.Tanner_graph
  • CodingTheory.Tanner_graph_plot
  • CodingTheory.TetraCode
  • CodingTheory.all_cyclotomic_cosets
  • CodingTheory.are_equivalent
  • CodingTheory.are_equivalent_basis
  • CodingTheory.are_symplectic_orthogonal
  • CodingTheory.augment
  • CodingTheory.average_ACE_distribution
  • CodingTheory.cardinality
  • CodingTheory.characteristic_polynomial
  • CodingTheory.check_concentrated_degree_distribution
  • CodingTheory.check_degree_distribution
  • CodingTheory.check_degree_polynomial
  • CodingTheory.circulants
  • CodingTheory.column_bound
  • CodingTheory.column_row_bounds
  • CodingTheory.complement_qcosets
  • CodingTheory.computation_graph
  • CodingTheory.concatenate
  • CodingTheory.concatenation_type
  • CodingTheory.coning
  • CodingTheory.construction_X
  • CodingTheory.construction_X3
  • CodingTheory.copying
  • CodingTheory.copying_as_coning
  • CodingTheory.coset_intersection
  • CodingTheory.count_short_cycles
  • CodingTheory.crossover_probability
  • CodingTheory.cycle_tetrahedron_group
  • CodingTheory.cyclotomic_coset
  • CodingTheory.defining_set
  • CodingTheory.degree_distributions
  • CodingTheory.degree_distributions_plot
  • CodingTheory.density_evolution
  • CodingTheory.density_lower_bound
  • CodingTheory.design_distance
  • CodingTheory.doubly_even_subcode
  • CodingTheory.dual_basis
  • CodingTheory.dual_defining_set
  • CodingTheory.dual_qcosets
  • CodingTheory.dual_scalars
  • CodingTheory.edge_vertex_incidence_graph
  • CodingTheory.edge_vertex_incidence_matrix
  • CodingTheory.edges
  • CodingTheory.encode
  • CodingTheory.entrywise_product_code
  • CodingTheory.erasure_probability
  • CodingTheory.evaluation_points
  • CodingTheory.even_subcode
  • CodingTheory.expand_matrix
  • CodingTheory.expanded_code
  • CodingTheory.expansion_basis
  • CodingTheory.expansion_dual_basis
  • CodingTheory.expansion_factor
  • CodingTheory.expurgate
  • CodingTheory.extract_bipartition
  • CodingTheory.field
  • CodingTheory.gauging
  • CodingTheory.gauging_as_coning
  • CodingTheory.generator_polynomial
  • CodingTheory.group_algebra_element_to_circulant_matrix
  • CodingTheory.hull
  • CodingTheory.idempotent
  • CodingTheory.inner_code
  • CodingTheory.is_Hermitian_LCD
  • CodingTheory.is_Hermitian_dual_containing
  • CodingTheory.is_Hermitian_self_dual
  • CodingTheory.is_Hermitian_self_orthogonal
  • CodingTheory.is_LCD
  • CodingTheory.is_MDS
  • CodingTheory.is_antiprimitive
  • CodingTheory.is_basis
  • CodingTheory.is_cyclic
  • CodingTheory.is_degenerate
  • CodingTheory.is_doubly_even
  • CodingTheory.is_dual_containing
  • CodingTheory.is_even
  • CodingTheory.is_extension
  • CodingTheory.is_fixed_point_free
  • CodingTheory.is_k_colorable
  • CodingTheory.is_narrowsense
  • CodingTheory.is_normal_basis
  • CodingTheory.is_orientable
  • CodingTheory.is_overcomplete
  • CodingTheory.is_primitive_basis
  • CodingTheory.is_reversible
  • CodingTheory.is_self_dual
  • CodingTheory.is_self_dual_basis
  • CodingTheory.is_self_orthogonal
  • CodingTheory.is_single_generator
  • CodingTheory.is_triorthogonal
  • CodingTheory.is_triply_even
  • CodingTheory.is_valid_bipartition
  • CodingTheory.juxtaposition
  • CodingTheory.lengthen
  • CodingTheory.limited
  • CodingTheory.median_ACE_distribution
  • CodingTheory.minimum_distance
  • CodingTheory.minimum_distance
  • CodingTheory.minimum_distance_lower_bound
  • CodingTheory.minimum_distance_upper_bound
  • CodingTheory.minimum_words
  • CodingTheory.mode_ACE_distribution
  • CodingTheory.multiplicative_gap_lower_bound
  • CodingTheory.noncirculant_generator_matrix
  • CodingTheory.noncirculant_parity_check_matrix
  • CodingTheory.nonzeros
  • CodingTheory.number_correctable_errors
  • CodingTheory.number_of_variables
  • CodingTheory.offset
  • CodingTheory.ord
  • CodingTheory.outer_code
  • CodingTheory.parity_check_matrix
  • CodingTheory.parity_check_polynomial
  • CodingTheory.permute_code
  • CodingTheory.plot_EXIT_chart
  • CodingTheory.polynomial_matrix
  • CodingTheory.polynomial_matrix_type
  • CodingTheory.primitive_basis
  • CodingTheory.primitive_root
  • CodingTheory.pseudoinverse
  • CodingTheory.puncture
  • CodingTheory.q_r_s_group
  • CodingTheory.qcoset_pairings
  • CodingTheory.qcosets
  • CodingTheory.qcosets_reps
  • CodingTheory.quadratic_residues
  • CodingTheory.quantum_weight_reduction
  • CodingTheory.r_s_group
  • CodingTheory.rate
  • CodingTheory.regular_LDPC_code
  • CodingTheory.relative_distance
  • CodingTheory.residue_polynomial_to_circulant_matrix
  • CodingTheory.row_bound
  • CodingTheory.row_supports
  • CodingTheory.row_supports_symplectic
  • CodingTheory.scalars
  • CodingTheory.set_distance_lower_bound!
  • CodingTheory.set_minimum_distance!
  • CodingTheory.shorten
  • CodingTheory.shortest_cycle_ACE
  • CodingTheory.shortest_cycles
  • CodingTheory.splitting_field
  • CodingTheory.standard_deviation
  • CodingTheory.standard_form_permutation
  • CodingTheory.star_tetrahedron_group
  • CodingTheory.strongly_lower_triangular_reduction
  • CodingTheory.subcode
  • CodingTheory.subcode_of_dimension_between_codes
  • CodingTheory.subfield_subcode
  • CodingTheory.symplectic_inner_product
  • CodingTheory.syndrome
  • CodingTheory.tetrahedron_group
  • CodingTheory.thickening_and_choose_heights
  • CodingTheory.trace_code
  • CodingTheory.triangle_group
  • CodingTheory.type
  • CodingTheory.type
  • CodingTheory.u_plus_w_v_plus_w_u_plus_v_plus_w
  • CodingTheory.u_u_plus_v
  • CodingTheory.variable_degree_distribution
  • CodingTheory.variable_degree_polynomial
  • CodingTheory.variance
  • CodingTheory.verify_dual_basis
  • CodingTheory.vertices
  • CodingTheory.weight_distribution
  • CodingTheory.weight_enumerator
  • CodingTheory.weight_matrix
  • CodingTheory.weight_plot
  • CodingTheory.weight_plot
  • CodingTheory.weight_reduction
  • CodingTheory.words
  • CodingTheory.words_of_weight
  • CodingTheory.words_of_weight
  • CodingTheory.wt
  • DataStructures.capacity
  • GroupsCore.order
  • Hecke.:⊗
  • Hecke.density
  • Hecke.dimension
  • Hecke.dual
  • Hecke.extend
  • Hecke.generators
  • Hecke.genus
  • Hecke.index
  • Hecke.is_primitive
  • Hecke.is_regular
  • Hecke.is_regular
  • Hecke.support
  • Hecke.support
  • LinearAlgebra.tr
  • Oscar.complement
  • Oscar.generator_matrix
  • Oscar.girth
  • Oscar.normal_subgroups
« References

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