Information on Result #702907
Linear OA(2217, 1090, F2, 40) (dual of [1090, 873, 41]-code), using construction XX applied to C1 = C([987,1022]), C2 = C([993,4]), C3 = C1 + C2 = C([993,1022]), and C∩ = C1 ∩ C2 = C([987,4]) based on
- linear OA(2175, 1023, F2, 36) (dual of [1023, 848, 37]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−36,−35,…,−1}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2171, 1023, F2, 35) (dual of [1023, 852, 36]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−30,−29,…,4}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−36,−35,…,4}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2150, 1023, F2, 30) (dual of [1023, 873, 31]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−30,−29,…,−1}, and designed minimum distance d ≥ |I|+1 = 31 [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, 31, F2, 4) (dual of [31, 21, 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(2218, 1091, F2, 41) (dual of [1091, 873, 42]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2217, 545, F2, 2, 40) (dual of [(545, 2), 873, 41]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2217, 218, F2, 5, 40) (dual of [(218, 5), 873, 41]-NRT-code) | [i] | ||