Information on Result #711829
Linear OA(5125, 672, F5, 35) (dual of [672, 547, 36]-code), using construction XX applied to C1 = C([126,156]), C2 = C([133,161]), C3 = C1 + C2 = C([133,156]), and C∩ = C1 ∩ C2 = C([126,161]) based on
- linear OA(595, 624, F5, 31) (dual of [624, 529, 32]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {126,127,…,156}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(593, 624, F5, 29) (dual of [624, 531, 30]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {133,134,…,161}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(5111, 624, F5, 36) (dual of [624, 513, 37]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {126,127,…,161}, and designed minimum distance d ≥ |I|+1 = 37 [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 = {133,134,…,156}, and designed minimum distance d ≥ |I|+1 = 25 [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, 20, F5, 3) (dual of [20, 16, 4]-code or 20-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 OA(5126, 673, F5, 35) (dual of [673, 547, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5125, 336, F5, 2, 35) (dual of [(336, 2), 547, 36]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(5125, 224, F5, 3, 35) (dual of [(224, 3), 547, 36]-NRT-code) | [i] | ||