Information on Result #702447
Linear OA(2211, 576, F2, 44) (dual of [576, 365, 45]-code), using construction XX applied to C1 = C([471,510]), C2 = C([477,4]), C3 = C1 + C2 = C([477,510]), and C∩ = C1 ∩ C2 = C([471,4]) based on
- linear OA(2171, 511, F2, 40) (dual of [511, 340, 41]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−40,−39,…,−1}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−34,−33,…,4}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−40,−39,…,4}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- 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(211, 36, F2, 4) (dual of [36, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 44, F2, 4) (dual of [44, 33, 5]-code), using
- linear OA(210, 29, F2, 4) (dual of [29, 19, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), 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(2213, 578, F2, 44) (dual of [578, 365, 45]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2214, 579, F2, 44) (dual of [579, 365, 45]-code) | [i] | ||
| 3 | Linear OA(2212, 577, F2, 45) (dual of [577, 365, 46]-code) | [i] | Adding a Parity Check Bit | |
| 4 | Linear OOA(2211, 288, F2, 2, 44) (dual of [(288, 2), 365, 45]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2211, 192, F2, 3, 44) (dual of [(192, 3), 365, 45]-NRT-code) | [i] | ||
| 6 | Linear OOA(2211, 144, F2, 4, 44) (dual of [(144, 4), 365, 45]-NRT-code) | [i] | ||