Information on Result #1436790
Linear OOA(557, 1953147, F5, 2, 8) (dual of [(1953147, 2), 3906237, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(557, 1953147, F5, 8) (dual of [1953147, 1953090, 9]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(556, 1953145, F5, 8) (dual of [1953145, 1953089, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(555, 1953125, F5, 8) (dual of [1953125, 1953070, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(519, 20, F5, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,5)), using
- dual of repetition code with length 20 [i]
- linear OA(51, 20, F5, 1) (dual of [20, 19, 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(556, 1953146, F5, 7) (dual of [1953146, 1953090, 8]-code), using Gilbert–Varšamov bound and bm = 556 > Vbs−1(k−1) = 315 813991 606188 492913 084489 524271 265957 [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(556, 1953145, F5, 8) (dual of [1953145, 1953089, 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(557, 976573, F5, 3, 8) (dual of [(976573, 3), 2929662, 9]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(557, 976573, F5, 10, 8) (dual of [(976573, 10), 9765673, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |