Information on Result #672931
Linear OA(2222, 2060, F2, 41) (dual of [2060, 1838, 42]-code), using construction X applied to Ce(40) ⊂ Ce(38) based on
- linear OA(2221, 2048, F2, 41) (dual of [2048, 1827, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2210, 2048, F2, 39) (dual of [2048, 1838, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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(2222, 2060, F2, 40) (dual of [2060, 1838, 41]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2223, 2061, F2, 41) (dual of [2061, 1838, 42]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2224, 2062, F2, 41) (dual of [2062, 1838, 42]-code) | [i] | ||
| 4 | Linear OA(2225, 2063, F2, 41) (dual of [2063, 1838, 42]-code) | [i] | ||
| 5 | Linear OA(2221, 2059, F2, 40) (dual of [2059, 1838, 41]-code) | [i] | Truncation | |
| 6 | Linear OOA(2222, 1030, F2, 2, 41) (dual of [(1030, 2), 1838, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2222, 686, F2, 3, 41) (dual of [(686, 3), 1836, 42]-NRT-code) | [i] | ||
| 8 | Linear OOA(2222, 515, F2, 4, 41) (dual of [(515, 4), 1838, 42]-NRT-code) | [i] | ||
| 9 | Linear OOA(2222, 412, F2, 5, 41) (dual of [(412, 5), 1838, 42]-NRT-code) | [i] | ||
| 10 | Linear OOA(2222, 343, F2, 6, 41) (dual of [(343, 6), 1836, 42]-NRT-code) | [i] | ||
| 11 | Linear OOA(2222, 294, F2, 7, 41) (dual of [(294, 7), 1836, 42]-NRT-code) | [i] | ||
| 12 | Linear OOA(2222, 257, F2, 8, 41) (dual of [(257, 8), 1834, 42]-NRT-code) | [i] | ||