Information on Result #711248
Linear OA(591, 669, F5, 24) (dual of [669, 578, 25]-code), using construction XX applied to C1 = C([136,155]), C2 = C([143,159]), C3 = C1 + C2 = C([143,155]), and C∩ = C1 ∩ C2 = C([136,159]) based on
- linear OA(564, 624, F5, 20) (dual of [624, 560, 21]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {136,137,…,155}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(557, 624, F5, 17) (dual of [624, 567, 18]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {143,144,…,159}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(577, 624, F5, 24) (dual of [624, 547, 25]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {136,137,…,159}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(544, 624, F5, 13) (dual of [624, 580, 14]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {143,144,…,155}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(510, 28, F5, 6) (dual of [28, 18, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [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(57, 25, F5, 4) (dual of [25, 18, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(51, 3, F5, 1) (dual of [3, 2, 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
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(54, 17, F5, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,5)), 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(591, 223, F5, 3, 24) (dual of [(223, 3), 578, 25]-NRT-code) | [i] | OOA Folding | |