Information on Result #701733
Linear OA(289, 295, F2, 21) (dual of [295, 206, 22]-code), using construction XX applied to C1 = C([237,0]), C2 = C([243,2]), C3 = C1 + C2 = C([243,0]), and C∩ = C1 ∩ C2 = C([237,2]) based on
- linear OA(269, 255, F2, 19) (dual of [255, 186, 20]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−18,−17,…,0}, and designed minimum distance d ≥ |I|+1 = 20 [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 = {−12,−11,…,2}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- 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 = {−18,−17,…,2}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(249, 255, F2, 13) (dual of [255, 206, 14]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−12,−11,…,0}, and designed minimum distance d ≥ |I|+1 = 14 [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(288, 294, F2, 20) (dual of [294, 206, 21]-code) | [i] | Truncation | |
| 2 | Linear OOA(289, 147, F2, 2, 21) (dual of [(147, 2), 205, 22]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(289, 98, F2, 3, 21) (dual of [(98, 3), 205, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(289, 73, F2, 4, 21) (dual of [(73, 4), 203, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(289, 59, F2, 5, 21) (dual of [(59, 5), 206, 22]-NRT-code) | [i] | ||