Information on Result #710832
Linear OA(522, 633, F5, 7) (dual of [633, 611, 8]-code), using construction XX applied to C1 = C([151,156]), C2 = C([153,157]), C3 = C1 + C2 = C([153,156]), and C∩ = C1 ∩ C2 = C([151,157]) based on
- linear OA(517, 624, F5, 6) (dual of [624, 607, 7]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {151,152,…,156}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(517, 624, F5, 5) (dual of [624, 607, 6]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {153,154,155,156,157}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(521, 624, F5, 7) (dual of [624, 603, 8]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {151,152,…,157}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(513, 624, F5, 4) (dual of [624, 611, 5]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {153,154,155,156}, and designed minimum distance d ≥ |I|+1 = 5 [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
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(522, 559, F5, 2, 7) (dual of [(559, 2), 1096, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(522, 559, F5, 3, 7) (dual of [(559, 3), 1655, 8]-NRT-code) | [i] | ||
| 3 | Digital (15, 22, 559)-net over F5 | [i] | ||
| 4 | Linear OA(523, 636, F5, 7) (dual of [636, 613, 8]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OOA(522, 316, F5, 2, 7) (dual of [(316, 2), 610, 8]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(522, 211, F5, 3, 7) (dual of [(211, 3), 611, 8]-NRT-code) | [i] | ||
| 7 | Linear OOA(522, 210, F5, 7, 7) (dual of [(210, 7), 1448, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |