Information on Result #710838
Linear OA(527, 638, F5, 8) (dual of [638, 611, 9]-code), using construction XX applied to C1 = C([622,3]), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([622,5]) based on
- linear OA(521, 624, F5, 6) (dual of [624, 603, 7]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,3}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(517, 624, F5, 6) (dual of [624, 607, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(525, 624, F5, 8) (dual of [624, 599, 9]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,5}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(513, 624, F5, 4) (dual of [624, 611, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 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
- linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
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 OA(528, 640, F5, 8) (dual of [640, 612, 9]-code) | [i] | Construction X with Varšamov Bound | |
| 2 | Linear OOA(527, 319, F5, 2, 8) (dual of [(319, 2), 611, 9]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(527, 212, F5, 3, 8) (dual of [(212, 3), 609, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(527, 159, F5, 8, 8) (dual of [(159, 8), 1245, 9]-NRT-code) | [i] | OA Folding and Stacking | |