Information on Result #701861
Linear OA(2123, 280, F2, 31) (dual of [280, 157, 32]-code), using construction XX applied to C1 = C([251,24]), C2 = C([0,26]), C3 = C1 + C2 = C([0,24]), and C∩ = C1 ∩ C2 = C([251,26]) based on
- linear OA(2109, 255, F2, 29) (dual of [255, 146, 30]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2101, 255, F2, 27) (dual of [255, 154, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2117, 255, F2, 31) (dual of [255, 138, 32]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,26}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(293, 255, F2, 25) (dual of [255, 162, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 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 OA(2122, 279, F2, 30) (dual of [279, 157, 31]-code) | [i] | Truncation | |
| 2 | Linear OOA(2123, 140, F2, 2, 31) (dual of [(140, 2), 157, 32]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2123, 93, F2, 3, 31) (dual of [(93, 3), 156, 32]-NRT-code) | [i] | ||