Information on Result #710829
Linear OA(528, 639, F5, 8) (dual of [639, 611, 9]-code), using construction XX applied to C1 = C([0,5]), C2 = C([3,7]), C3 = C1 + C2 = C([3,5]), and C∩ = C1 ∩ C2 = C([0,7]) based on
- 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(520, 624, F5, 5) (dual of [624, 604, 6]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {3,4,5,6,7}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(525, 624, F5, 8) (dual of [624, 599, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(512, 624, F5, 3) (dual of [624, 612, 4]-code or 624-cap in PG(11,5)), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {3,4,5}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [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
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, 213, F5, 3, 8) (dual of [(213, 3), 611, 9]-NRT-code) | [i] | OOA Folding | |