Information on Result #712281
Linear OA(5147, 664, F5, 43) (dual of [664, 517, 44]-code), using construction XX applied to C1 = C([116,156]), C2 = C([123,158]), C3 = C1 + C2 = C([123,156]), and C∩ = C1 ∩ C2 = C([116,158]) based on
- linear OA(5127, 624, F5, 41) (dual of [624, 497, 42]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {116,117,…,156}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(5115, 624, F5, 36) (dual of [624, 509, 37]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {123,124,…,158}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(5135, 624, F5, 43) (dual of [624, 489, 44]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {116,117,…,158}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(5107, 624, F5, 34) (dual of [624, 517, 35]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {123,124,…,156}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(511, 31, F5, 6) (dual of [31, 20, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- linear OA(59, 25, F5, 6) (dual of [25, 16, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(55, 25, F5, 3) (dual of [25, 20, 4]-code or 25-cap in PG(4,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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]
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- 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(5147, 332, F5, 2, 43) (dual of [(332, 2), 517, 44]-NRT-code) | [i] | OOA Folding | |