Information on Result #1436450
Linear OOA(538, 430, F5, 2, 12) (dual of [(430, 2), 822, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(538, 430, F5, 12) (dual of [430, 392, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(538, 633, F5, 12) (dual of [633, 595, 13]-code), using
- construction XX applied to C1 = C([146,156]), C2 = C([148,157]), C3 = C1 + C2 = C([148,156]), and C∩ = C1 ∩ C2 = C([146,157]) [i] based on
- linear OA(533, 624, F5, 11) (dual of [624, 591, 12]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {146,147,…,156}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(533, 624, F5, 10) (dual of [624, 591, 11]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {148,149,…,157}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(537, 624, F5, 12) (dual of [624, 587, 13]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {146,147,…,157}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(529, 624, F5, 9) (dual of [624, 595, 10]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {148,149,…,156}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- linear OA(50, 4, F5, 0) (dual of [4, 4, 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
- construction XX applied to C1 = C([146,156]), C2 = C([148,157]), C3 = C1 + C2 = C([148,156]), and C∩ = C1 ∩ C2 = C([146,157]) [i] based on
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(538, 215, F5, 3, 12) (dual of [(215, 3), 607, 13]-NRT-code) | [i] | OOA Folding | |