Information on Result #661464
Linear OA(2227, 335, F2, 67) (dual of [335, 108, 68]-code), using concatenation of two codes based on
- linear OA(1640, 67, F16, 33) (dual of [67, 27, 34]-code), using
- construction X applied to AG(F,30P) ⊂ AG(F,32P) [i] based on
- linear OA(1639, 64, F16, 33) (dual of [64, 25, 34]-code), using algebraic-geometric code AG(F,30P) [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(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(1639, 64, F16, 33) (dual of [64, 25, 34]-code), using algebraic-geometric code AG(F,30P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,30P) ⊂ 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
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(2227, 335, F2, 66) (dual of [335, 108, 67]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2228, 336, F2, 67) (dual of [336, 108, 68]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2229, 337, F2, 67) (dual of [337, 108, 68]-code) | [i] | ||
| 4 | Linear OA(2230, 338, F2, 67) (dual of [338, 108, 68]-code) | [i] | ||
| 5 | Linear OA(2231, 339, F2, 67) (dual of [339, 108, 68]-code) | [i] | ||
| 6 | Linear OA(2232, 340, F2, 67) (dual of [340, 108, 68]-code) | [i] | ||
| 7 | Linear OA(2226, 334, F2, 66) (dual of [334, 108, 67]-code) | [i] | Truncation | |
| 8 | Linear OA(2237, 350, F2, 66) (dual of [350, 113, 67]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OOA(2227, 167, F2, 2, 67) (dual of [(167, 2), 107, 68]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(2227, 111, F2, 3, 67) (dual of [(111, 3), 106, 68]-NRT-code) | [i] | ||