Information on Result #682146
Linear OA(528, 1953134, F5, 4) (dual of [1953134, 1953106, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(528, 1953125, F5, 4) (dual of [1953125, 1953097, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(519, 1953125, F5, 3) (dual of [1953125, 1953106, 4]-code or 1953125-cap in PG(18,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(50, 9, F5, 0) (dual of [9, 9, 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
Mode: Constructive and 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(528, 1953134, F5, 2, 4) (dual of [(1953134, 2), 3906240, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(528, 1953134, F5, 3, 4) (dual of [(1953134, 3), 5859374, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(528, 976567, F5, 2, 4) (dual of [(976567, 2), 1953106, 5]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(528, 976567, F5, 3, 4) (dual of [(976567, 3), 2929673, 5]-NRT-code) | [i] | OA Folding and Stacking | |