Information on Result #2226637
Linear OA(2236, 344, F2, 68) (dual of [344, 108, 69]-code), using 1 times truncation based on linear OA(2237, 345, F2, 69) (dual of [345, 108, 70]-code), using
- concatenation of two codes [i] based on
- linear OA(1642, 69, F16, 34) (dual of [69, 27, 35]-code), using
- construction X applied to AG(F,29P) ⊂ AG(F,32P) [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(1637, 64, F16, 31) (dual of [64, 27, 32]-code), using algebraic-geometric code AG(F,32P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(162, 5, F16, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), 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,32P) [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(1642, 69, F16, 34) (dual of [69, 27, 35]-code), using
Mode: Constructive and 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(2238, 346, F2, 68) (dual of [346, 108, 69]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2239, 347, F2, 68) (dual of [347, 108, 69]-code) | [i] | ||
| 3 | Linear OA(2240, 348, F2, 68) (dual of [348, 108, 69]-code) | [i] | ||
| 4 | Linear OA(2241, 349, F2, 68) (dual of [349, 108, 69]-code) | [i] | ||
| 5 | Linear OA(2240, 350, F2, 68) (dual of [350, 110, 69]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(2241, 352, F2, 68) (dual of [352, 111, 69]-code) | [i] | ||
| 7 | Linear OA(2239, 348, F2, 68) (dual of [348, 109, 69]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(2241, 351, F2, 68) (dual of [351, 110, 69]-code) | [i] | ||
| 9 | Linear OOA(2236, 172, F2, 2, 68) (dual of [(172, 2), 108, 69]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(2236, 114, F2, 3, 68) (dual of [(114, 3), 106, 69]-NRT-code) | [i] | ||