Information on Result #711520
Linear OA(5115, 678, F5, 31) (dual of [678, 563, 32]-code), using construction XX applied to C1 = C([141,166]), C2 = C([136,159]), C3 = C1 + C2 = C([141,159]), and C∩ = C1 ∩ C2 = C([136,166]) based on
- linear OA(581, 624, F5, 26) (dual of [624, 543, 27]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {141,142,…,166}, and designed minimum distance d ≥ |I|+1 = 27 [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(597, 624, F5, 31) (dual of [624, 527, 32]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {136,137,…,166}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(561, 624, F5, 19) (dual of [624, 563, 20]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {141,142,…,159}, and designed minimum distance d ≥ |I|+1 = 20 [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(57, 23, F5, 4) (dual of [23, 16, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), 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(5115, 339, F5, 2, 31) (dual of [(339, 2), 563, 32]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5115, 226, F5, 3, 31) (dual of [(226, 3), 563, 32]-NRT-code) | [i] | ||