Information on Result #1438692
Linear OOA(5114, 78162, F5, 2, 19) (dual of [(78162, 2), 156210, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5114, 78162, F5, 19) (dual of [78162, 78048, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5113, 78160, F5, 19) (dual of [78160, 78047, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(578, 78125, F5, 14) (dual of [78125, 78047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(5113, 78161, F5, 18) (dual of [78161, 78048, 19]-code), using Gilbert–Varšamov bound and bm = 5113 > Vbs−1(k−1) = 7 310659 983456 097784 627056 822724 487846 610293 560919 826415 924559 831449 062094 899905 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(5113, 78160, F5, 19) (dual of [78160, 78047, 20]-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(5114, 39081, F5, 3, 19) (dual of [(39081, 3), 117129, 20]-NRT-code) | [i] | OOA Folding | |