Information on Result #1447774
Linear OOA(8157, 2097205, F8, 2, 24) (dual of [(2097205, 2), 4194253, 25]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8157, 2097205, F8, 24) (dual of [2097205, 2097048, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8155, 2097201, F8, 24) (dual of [2097201, 2097046, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(87, 49, F8, 5) (dual of [49, 42, 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(24) ⊂ Ce(17) [i] based on
- linear OA(8155, 2097203, F8, 23) (dual of [2097203, 2097048, 24]-code), using Gilbert–Varšamov bound and bm = 8155 > Vbs−1(k−1) = 41440 872736 745127 272002 774503 496160 501227 956327 177782 565907 077514 283975 281604 543243 517213 130336 527517 439568 024077 374150 980318 972194 693584 [i]
- linear OA(80, 2, F8, 0) (dual of [2, 2, 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(8155, 2097201, F8, 24) (dual of [2097201, 2097046, 25]-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(8157, 1048602, F8, 3, 24) (dual of [(1048602, 3), 3145649, 25]-NRT-code) | [i] | OOA Folding | |