Information on Result #702336
Linear OA(2166, 550, F2, 37) (dual of [550, 384, 38]-code), using construction XX applied to C1 = C([477,0]), C2 = C([483,2]), C3 = C1 + C2 = C([483,0]), and C∩ = C1 ∩ C2 = C([477,2]) based on
- linear OA(2145, 511, F2, 35) (dual of [511, 366, 36]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−34,−33,…,0}, and designed minimum distance d ≥ |I|+1 = 36 [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 = {−28,−27,…,2}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- 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 = {−34,−33,…,2}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2127, 511, F2, 29) (dual of [511, 384, 30]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−28,−27,…,0}, and designed minimum distance d ≥ |I|+1 = 30 [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(21, 10, F2, 1) (dual of [10, 9, 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(2165, 549, F2, 36) (dual of [549, 384, 37]-code) | [i] | Truncation | |
| 2 | Linear OOA(2166, 275, F2, 2, 37) (dual of [(275, 2), 384, 38]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2166, 183, F2, 3, 37) (dual of [(183, 3), 383, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(2166, 137, F2, 4, 37) (dual of [(137, 4), 382, 38]-NRT-code) | [i] | ||
| 5 | Linear OOA(2166, 110, F2, 5, 37) (dual of [(110, 5), 384, 38]-NRT-code) | [i] | ||