- Introduction
- Constructions for Z4 Codes
- The Gray Map
- Families of Codes over Z4
- KerdockCode(m): RngIntElt -> Code
- PreparataCode(m): RngIntElt -> Code
- ReedMullerCodeZ4(r, m) : RngIntElt, RngIntElt -> Code
- GoethalsCode(m) : RngIntElt -> Code
- DelsarteGoethalsCode(m, delta) : RngIntElt, RngIntElt -> Code
- GoethalsDelsarteCode(m, delta) : RngIntElt, RngIntElt -> Code
- QRCodeZ4(p) : RngIntElt -> Code
- GolayCodeZ4(e) : BoolElt -> Code
- SimplexAlphaCodeZ4(k) : RngIntElt -> Code
- SimplexBetaCodeZ4(k) : RngIntElt -> Code
- Example CodeZ4_Kerdock (H165E2)
- HadamardCodeZ4(δ, m) : RngIntElt, RngIntElt -> CodeLinRng, Mtrx
- ExtendedPerfectCodeZ4(δ, m) : RngIntElt, RngIntElt -> CodeLinRng, Mtrx
- Example CodeZ4_spain-Z4-1 (H165E3)
- ReedMullerCodeZ4(r, m) : RngIntElt, RngIntElt -> CodeLinRng
- ReedMullerCodesLRMZ4(r, m) : RngIntElt, RngIntElt -> SeqEnum
- ReedMullerCodeRMZ4(s, r, m) : RngIntElt, RngIntElt, RngIntElt -> CodeLinRng, Mtrx
- Example CodeZ4_spain-Z4-2 (H165E4)
- ReedMullerCodesRMZ4(s, m) : RngIntElt, RngIntElt -> Tup
- Example CodeZ4_spain-Z4-3 (H165E5)
- Derived Binary Codes
- New Codes from Old
- PlotkinSum(A, B) : Mtrx, Mtrx -> Mtrx
- PlotkinSum(C, D) : Code, Code -> Code
- QuaternaryPlotkinSum(A, B) : Mtrx, Mtrx -> Mtrx
- QuaternaryPlotkinSum(C, D) : Code, Code -> Code
- BQPlotkinSum(A, B, C) : Mtrx, Mtrx, Mtrx -> Mtrx
- BQPlotkinSum(D, E, F) : Code, Code, Code -> Code
- DoublePlotkinSum(A, B, C, D) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx
- DoublePlotkinSum(E, F, G, H) : Code, Code, Code, Code -> Code
- DualKroneckerZ4(C) : CodeLinRng -> CodeLinRng
- Example CodeZ4_spain-Z4-4 (H165E7)
- Example CodeZ4_spain-Z4-4a (H165E8)
- Invariants
- Weight Distributions
- Weight Enumerators
- Decoding
- Coset Decoding
- Syndrome Decoding
- Lifted Decoding
- Permutation Decoding
- IsPermutationDecodeSet(C, I, S, s) : CodeLinRng, [RngIntElt], [GrpPermElt], RngIntElt -> BoolElt
- PermutationDecode(C, I, S, s, u) : CodeLinRng, [RngIntElt], [GrpPermElt], RngIntElt, ModTupFldElt -> BoolElt, ModTupRngElt, ModTupFldElt
- PermutationDecode(C, I, S, s, Q) : CodeLinRng, [RngIntElt], [GrpPermElt], RngIntElt, [ModTupFldElt] -> [BoolElt], [ModTupRngElt], [ModTupFldElt]
- Example CodeZ4_spain-Z4-15 (H165E23)
- PDSetHadamardCodeZ4(δ, m) : RngIntElt, RngIntElt -> SeqEnum, SeqEnum, SeqEnum, SeqEnum, SeqEnum
- PDSetKerdockCodeZ4(m) : RngIntElt -> SeqEnum, SeqEnum, SeqEnum, SeqEnum
- Example CodeZ4_spain-Z4-16 (H165E24)
- Automorphism Groups
- PermutationGroupHadamardCodeZ4(δ, m) : RngIntElt, RngIntElt -> GrpPerm, Mtrx
- PermutationGroupHadamardCodeZ4Order(δ, m) : RngIntElt, RngIntElt -> RngIntElt
- PermutationGroupExtendedPerfectCodeZ4(δ, m) : RngIntElt, RngIntElt -> GrpPerm, Mtrx
- PermutationGroupExtendedPerfectCodeZ4Order(δ, m) : RngIntElt, RngIntElt -> RngIntElt
- Example CodeZ4_spain-Z4-8 (H165E25)
- PermutationGroup(C) : CodeLinRng -> GrpPerm
- PermutationGroupGrayMapImage(C) : CodeLinRng -> GrpPerm
- Example CodeZ4_code-z4-perm-group (H165E26)
- Bibliography
V2.28, 13 July 2023