Information on Result #1316333
Linear OA(1682, 1048603, F16, 17) (dual of [1048603, 1048521, 18]-code), using construction X with Varšamov bound based on
- linear OA(1681, 1048601, F16, 17) (dual of [1048601, 1048520, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1656, 1048576, F16, 12) (dual of [1048576, 1048520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(165, 25, F16, 4) (dual of [25, 20, 5]-code), using
- extended algebraic-geometric code AGe(F,20P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 25, using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(1681, 1048602, F16, 16) (dual of [1048602, 1048521, 17]-code), using Gilbert–Varšamov bound and bm = 1681 > Vbs−1(k−1) = 682307 608916 241845 176724 097322 594486 024916 893402 078420 603010 808821 785212 013268 341951 356653 484016 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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 OOA(1682, 1048603, F16, 2, 17) (dual of [(1048603, 2), 2097124, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (65, 82, 1048603)-net over F16 | [i] | ||