Information on Result #1437052
Linear OOA(568, 1953157, F5, 2, 9) (dual of [(1953157, 2), 3906246, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(568, 1953157, F5, 9) (dual of [1953157, 1953089, 10]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(567, 1953155, F5, 9) (dual of [1953155, 1953088, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(564, 1953125, F5, 9) (dual of [1953125, 1953061, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(53, 30, F5, 2) (dual of [30, 27, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(567, 1953156, F5, 8) (dual of [1953156, 1953089, 9]-code), using Gilbert–Varšamov bound and bm = 567 > Vbs−1(k−1) = 352 486177 137451 133912 994108 051498 624472 670845 [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(567, 1953155, F5, 9) (dual of [1953155, 1953088, 10]-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(568, 976578, F5, 3, 9) (dual of [(976578, 3), 2929666, 10]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(568, 976578, F5, 10, 9) (dual of [(976578, 10), 9765712, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |