Information on Result #701746
Linear OA(297, 295, F2, 23) (dual of [295, 198, 24]-code), using construction XX applied to C1 = C([235,0]), C2 = C([241,2]), C3 = C1 + C2 = C([241,0]), and C∩ = C1 ∩ C2 = C([235,2]) based on
- linear OA(277, 255, F2, 21) (dual of [255, 178, 22]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−20,−19,…,0}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(265, 255, F2, 17) (dual of [255, 190, 18]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−14,−13,…,2}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(285, 255, F2, 23) (dual of [255, 170, 24]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−20,−19,…,2}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(257, 255, F2, 15) (dual of [255, 198, 16]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−14,−13,…,0}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(211, 31, F2, 5) (dual of [31, 20, 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(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(296, 294, F2, 22) (dual of [294, 198, 23]-code) | [i] | Truncation | |
| 2 | Linear OOA(297, 147, F2, 2, 23) (dual of [(147, 2), 197, 24]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(297, 98, F2, 3, 23) (dual of [(98, 3), 197, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(297, 73, F2, 4, 23) (dual of [(73, 4), 195, 24]-NRT-code) | [i] | ||