- Introduction
- Constructions
- General Linear Codes
- Simple Linear Codes
- ZeroCode(R, n) : Rng, RngIntElt -> Code
- RepetitionCode(R, n) : Rng, RngIntElt -> Code
- ZeroSumCode(R, n) : Rng, RngIntElt -> Code
- UniverseCode(R, n) : Rng, RngIntElt -> Code
- RandomLinearCode(R, n, k) : Rng, RngIntElt, RngIntElt -> Code
- Example CodeRng_simple-finite-ring (H164E4)
- General Cyclic Codes
- Invariants
- Subcodes
- Boolean Predicates
- New Codes from Old
- Sum, Intersection and Dual
- Standard Constructions
- DirectSum(C, D) : Code, Code -> Code
- DirectProduct(C, D) : Code, Code -> Code
- C1 cat C2 : Code,Code -> Code
- ExtendCode(C) : Code -> Code
- ExtendCode(C, n) : Code, RngIntElt -> Code
- PadCode(C, n) : Code, RngIntElt -> Code
- PlotkinSum(C, D) : Code, Code -> Code
- PunctureCode(C, i) : Code, RngIntElt -> Code
- PunctureCode(C, S) : Code, { RngIntElt } -> Code
- ShortenCode(C, i) : Code, RngIntElt -> Code
- ShortenCode(C, S) : Code, { RngIntElt } -> Code
- Example CodeRng_lengths (H164E10)
- Example CodeRng_punct-z4 (H164E11)
- Codeword Operations
- Construction
- Operations
- u + v : ModTupRngElt, ModTupRngElt -> ModTupRngElt
- - u : ModTupRngElt -> ModTupRngElt
- u - v : ModTupRngElt, ModTupRngElt -> ModTupRngElt
- a * u : RngElt, ModTupRngElt -> ModTupRngElt
- Weight(v) : ModTupRngElt -> RngIntElt
- Distance(u, v) : ModTupRngElt, ModTupRngElt -> RngIntElt
- Support(w) : ModTupRngElt -> { RngIntElt }
- (u, v) : ModTupRngElt, ModTupRngElt -> RngElt
- Coordinates(C, u) : Code, ModTupRngElt -> [ RngFinElt ]
- Normalize(u) : ModTupRngElt -> ModTupRngElt
- Rotate(u, k) : ModTupRngElt, RngIntElt -> ModTupRngElt
- Rotate(~u, k) : ModTupRngElt, RngIntElt ->
- Parent(w): ModTupRngElt -> ModTupRng
- Example CodeRng_codeword-ops (H164E13)
- Accessing Components of a Codeword
- Weight Distributions
- Weight Enumerators
- Bibliography
V2.28, 13 July 2023