Information on Result #702334
Linear OA(2166, 551, F2, 36) (dual of [551, 385, 37]-code), using construction XX applied to C1 = C([477,510]), C2 = C([483,2]), C3 = C1 + C2 = C([483,510]), and C∩ = C1 ∩ C2 = C([477,2]) based on
- linear OA(2144, 511, F2, 34) (dual of [511, 367, 35]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−34,−33,…,−1}, and designed minimum distance d ≥ |I|+1 = 35 [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(2126, 511, F2, 28) (dual of [511, 385, 29]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−28,−27,…,−1}, and designed minimum distance d ≥ |I|+1 = 29 [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, 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(2170, 555, F2, 36) (dual of [555, 385, 37]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2167, 552, F2, 37) (dual of [552, 385, 38]-code) | [i] | Adding a Parity Check Bit | |
| 3 | Linear OOA(2166, 275, F2, 2, 36) (dual of [(275, 2), 384, 37]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2166, 110, F2, 5, 36) (dual of [(110, 5), 384, 37]-NRT-code) | [i] | ||