Information on Result #1445327
Linear OOA(8114, 2097196, F8, 2, 18) (dual of [(2097196, 2), 4194278, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8114, 2097196, F8, 18) (dual of [2097196, 2097082, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8113, 2097194, F8, 18) (dual of [2097194, 2097081, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(87, 42, F8, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- linear OA(8113, 2097195, F8, 17) (dual of [2097195, 2097082, 18]-code), using Gilbert–Varšamov bound and bm = 8113 > Vbs−1(k−1) = 222403 887578 561040 312467 217876 825338 896621 996501 283819 858536 510723 730367 809214 341161 413392 825129 410866 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(8113, 2097194, F8, 18) (dual of [2097194, 2097081, 19]-code), 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(8114, 1048598, F8, 3, 18) (dual of [(1048598, 3), 3145680, 19]-NRT-code) | [i] | OOA Folding | |