Information on Result #1297603
Linear OA(2234, 339, F2, 68) (dual of [339, 105, 69]-code), using construction X with Varšamov bound based on
- linear OA(2230, 334, F2, 68) (dual of [334, 104, 69]-code), using
- 1 times truncation [i] based on linear OA(2231, 335, F2, 69) (dual of [335, 104, 70]-code), using
- concatenation of two codes [i] based on
- linear OA(1641, 67, F16, 34) (dual of [67, 26, 35]-code), using
- construction X applied to AG(F,29P) ⊂ AG(F,31P) [i] based on
- linear OA(1640, 64, F16, 34) (dual of [64, 24, 35]-code), using algebraic-geometric code AG(F,29P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OA(1638, 64, F16, 32) (dual of [64, 26, 33]-code), using algebraic-geometric code AG(F,31P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(161, 3, F16, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(1640, 64, F16, 34) (dual of [64, 24, 35]-code), using algebraic-geometric code AG(F,29P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,29P) ⊂ AG(F,31P) [i] based on
- linear OA(21, 5, F2, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(1641, 67, F16, 34) (dual of [67, 26, 35]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2231, 335, F2, 69) (dual of [335, 104, 70]-code), using
- linear OA(2230, 335, F2, 64) (dual of [335, 105, 65]-code), using Gilbert–Varšamov bound and bm = 2230 > Vbs−1(k−1) = 1252 806069 547850 460129 221588 350208 668113 688154 171957 483077 644008 812384 [i]
- linear OA(23, 4, F2, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,2) or 4-cap in PG(2,2)), using
- dual of repetition code with length 4 [i]
- caps in base b = 2 [i]
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2235, 340, F2, 69) (dual of [340, 105, 70]-code) | [i] | Adding a Parity Check Bit | |