Information on Result #702850
Linear OA(2188, 1067, F2, 37) (dual of [1067, 879, 38]-code), using construction XX applied to C1 = C([989,0]), C2 = C([995,2]), C3 = C1 + C2 = C([995,0]), and C∩ = C1 ∩ C2 = C([989,2]) based on
- linear OA(2166, 1023, F2, 35) (dual of [1023, 857, 36]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−34,−33,…,0}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2151, 1023, F2, 31) (dual of [1023, 872, 32]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−28,−27,…,2}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−34,−33,…,2}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2141, 1023, F2, 29) (dual of [1023, 882, 30]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−28,−27,…,0}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33 | 210−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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(2187, 1066, F2, 36) (dual of [1066, 879, 37]-code) | [i] | Truncation | |
| 2 | Linear OOA(2188, 533, F2, 2, 37) (dual of [(533, 2), 878, 38]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2188, 355, F2, 3, 37) (dual of [(355, 3), 877, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(2188, 266, F2, 4, 37) (dual of [(266, 4), 876, 38]-NRT-code) | [i] | ||
| 5 | Linear OOA(2188, 213, F2, 5, 37) (dual of [(213, 5), 877, 38]-NRT-code) | [i] | ||
| 6 | Linear OOA(2188, 177, F2, 6, 37) (dual of [(177, 6), 874, 38]-NRT-code) | [i] | ||
| 7 | Linear OOA(2188, 152, F2, 7, 37) (dual of [(152, 7), 876, 38]-NRT-code) | [i] | ||
| 8 | Linear OOA(2188, 133, F2, 8, 37) (dual of [(133, 8), 876, 38]-NRT-code) | [i] | ||