- Introduction
- Construction of Additive Codes
- Construction of General Additive Codes
- Some Trivial Additive Codes
- AdditiveZeroCode(F, K, n) : FldFin, FldFin, RngIntElt -> CodeAdd
- AdditiveRepetitionCode(F, K, n) : FldFin, FldFin, RngIntElt -> Code
- AdditiveZeroSumCode(F, K, n) : FldFin, FldFin, RngIntElt -> Code
- AdditiveUniverseCode(F, K, n) : FldFin,FldFin, RngIntElt -> Code
- RandomAdditiveCode(F, K, n, k) : FldFin,FldFin, RngIntElt, RngIntElt -> Code
- Example CodeAdd_SimpleCodeChain (H166E5)
- Invariants of an Additive Code
- Operations on Codewords
- Construction of a Codeword
- Arithmetic Operations on Codewords
- Distance and Weight
- Vector Space and Related Operations
- (u, v) : ModTupRngElt, ModTupRngElt -> RngElt
- TraceInnerProduct(K, u, v) : FldFin, ModTupFldElt, ModTupFldElt -> FldFinElt
- Support(w) : ModTupRngElt -> { RngIntElt }
- Coordinates(C, u) : Code, ModTupRngElt -> [ RngFinElt ]
- Parent(w): ModTupRngElt -> ModTupRng
- Rotate(u, k) : ModTupRngElt, RngIntElt -> ModTupRngElt
- Rotate(~u, k) : ModTupRngElt, RngIntElt ->
- Trace(u, S) : ModTupFldElt, FldFin -> ModTupFldElt
- Predicates for Codewords
- Accessing Components of a Codeword
- Subcodes
- The Subcode Constructor
- sub<C | L> : CodeAdd, List -> CodeAdd
- Subcode(C, k) : CodeAdd, RngIntElt -> CodeAdd
- Subcode(C, S) : CodeAdd, { RngIntElt } -> Code
- SubcodeBetweenCode(C1, C2, k) : CodeAdd, CodeAdd, RngIntElt -> CodeAdd
- SubcodeWordsOfWeight(C, w) : CodeAdd, RngIntElt -> CodeAdd
- SubcodeWordsOfWeight(C, S) : CodeAdd, { RngIntElt } -> CodeAdd
- Example CodeAdd_SubcodeBetweenCode (H166E7)
- Sum, Intersection and Dual
- Membership and Equality
- Properties of Codes
- The Weight Distribution
- Families of Linear Codes
- New Codes from Old
- Standard Constructions
- AugmentCode(C) : CodeAdd -> Code
- CodeComplement(C, S) : Code, Code -> Code
- DirectSum(C, D) : Code, Code -> Code
- DirectSum(Q) : [Code] -> Code
- DirectProduct(C, D) : Code, Code -> Code
- ExtendCode(C) : CodeAdd -> CodeAdd
- ExtendCode(C, n) : Code, RngIntElt -> Code
- PadCode(C, n) : CodeAdd, RngIntElt -> CodeAdd
- PlotkinSum(C1, C2) : Code, Code -> Code
- PlotkinSum(C1, C2, C3: parameters) : Code,Code,Code -> Code
- PunctureCode(C, i) : CodeAdd, RngIntElt -> Code
- PunctureCode(C, S) : CodeAdd, { RngIntElt } -> Code
- ShortenCode(C, i) : Code, RngIntElt -> Code
- ShortenCode(C, S) : Code, { RngIntElt } -> Code
- Combining Codes
- Automorphism Group
V2.28, 13 July 2023