Information on Result #1436583
Linear OOA(546, 78145, F5, 2, 8) (dual of [(78145, 2), 156244, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(546, 78145, F5, 8) (dual of [78145, 78099, 9]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(544, 78141, F5, 8) (dual of [78141, 78097, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(515, 16, F5, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,5)), using
- dual of repetition code with length 16 [i]
- linear OA(51, 16, F5, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(544, 78143, F5, 7) (dual of [78143, 78099, 8]-code), using Gilbert–Varšamov bound and bm = 544 > Vbs−1(k−1) = 1 294969 547630 666846 669090 746153 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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(544, 78141, F5, 8) (dual of [78141, 78097, 9]-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(546, 39072, F5, 3, 8) (dual of [(39072, 3), 117170, 9]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(546, 39072, F5, 10, 8) (dual of [(39072, 10), 390674, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |