Information on Result #702389
Linear OA(2189, 564, F2, 41) (dual of [564, 375, 42]-code), using construction XX applied to C1 = C([475,0]), C2 = C([481,4]), C3 = C1 + C2 = C([481,0]), and C∩ = C1 ∩ C2 = C([475,4]) based on
- linear OA(2154, 511, F2, 37) (dual of [511, 357, 38]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−36,−35,…,0}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2154, 511, F2, 35) (dual of [511, 357, 36]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−30,−29,…,4}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2172, 511, F2, 41) (dual of [511, 339, 42]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−36,−35,…,4}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2136, 511, F2, 31) (dual of [511, 375, 32]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−30,−29,…,0}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(211, 29, F2, 5) (dual of [29, 18, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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(2188, 563, F2, 40) (dual of [563, 375, 41]-code) | [i] | Truncation | |
| 2 | Linear OOA(2189, 282, F2, 2, 41) (dual of [(282, 2), 375, 42]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2189, 188, F2, 3, 41) (dual of [(188, 3), 375, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(2189, 141, F2, 4, 41) (dual of [(141, 4), 375, 42]-NRT-code) | [i] | ||