.. _sage.coding: Coding Theory ============= Coding theory is the mathematical theory for algebraic and combinatorial codes used for forward error correction in communications theory. Sage provides an extensive library of objects and algorithms in coding theory. Basic objects in coding theory are codes, channels, encoders, and decoders. The following modules provide the base classes defining them. .. toctree:: :maxdepth: 1 sage/coding/abstract_code sage/coding/channel sage/coding/encoder sage/coding/decoder Catalogs for available constructions of the basic objects and for bounds on the parameters of linear codes are provided. .. toctree:: :maxdepth: 1 sage/coding/channels_catalog sage/coding/codes_catalog sage/coding/decoders_catalog sage/coding/encoders_catalog sage/coding/bounds_catalog Linear Codes ------------ The following module is a base class for linear code objects regardless their metric. .. toctree:: :maxdepth: 1 sage/coding/linear_code_no_metric There is a number of representatives of linear codes over a specific metric. .. toctree:: :maxdepth: 1 sage/coding/linear_code sage/coding/linear_rank_metric Families of Linear Codes ------------------------ Famous families of codes, listed below, are represented in Sage by their own classes. For some of them, implementations of special decoding algorithms or computations for structural invariants are available. .. toctree:: :maxdepth: 1 sage/coding/parity_check_code sage/coding/hamming_code sage/coding/cyclic_code sage/coding/bch_code sage/coding/golay_code sage/coding/reed_muller_code sage/coding/grs_code sage/coding/goppa_code sage/coding/kasami_codes sage/coding/ag_code sage/coding/gabidulin_code .. toctree:: :hidden: sage/coding/ag_code_decoders In contrast, for some code families Sage can only construct their generator matrix and has no other a priori knowledge on them: .. toctree:: :maxdepth: 1 sage/coding/code_constructions sage/coding/guava sage/coding/self_dual_codes sage/coding/binary_code Derived Code Constructions -------------------------- Sage supports the following derived code constructions. If the constituent code is from a special code family, the derived codes inherit structural properties like decoding radius or minimum distance: .. toctree:: :maxdepth: 1 sage/coding/subfield_subcode sage/coding/punctured_code sage/coding/extended_code Other derived constructions that simply produce the modified generator matrix can be found among the methods of a constructed code. Decoding -------- Information-set decoding for linear codes: .. toctree:: :maxdepth: 1 sage/coding/information_set_decoder Guruswami-Sudan interpolation-based list decoding for Reed-Solomon codes: .. toctree:: :maxdepth: 1 sage/coding/guruswami_sudan/gs_decoder sage/coding/guruswami_sudan/interpolation sage/coding/guruswami_sudan/utils Automorphism Groups of Linear Codes ----------------------------------- .. toctree:: :maxdepth: 1 sage/coding/codecan/codecan sage/coding/codecan/autgroup_can_label Bounds for Parameters of Linear Codes ------------------------------------- .. toctree:: :maxdepth: 1 sage/coding/code_bounds sage/coding/delsarte_bounds Databases for Coding Theory --------------------------- .. toctree:: :maxdepth: 1 sage/coding/databases sage/coding/two_weight_db Miscellaneous Modules --------------------- There is at least one module in Sage for source coding in communications theory: .. toctree:: :maxdepth: 1 sage/coding/source_coding/huffman .. include:: ../footer.txt
