Information on Result #2175107
Linear OA(2178, 1061, F2, 35) (dual of [1061, 883, 36]-code), using adding a parity check bit based on linear OA(2177, 1060, F2, 34) (dual of [1060, 883, 35]-code), using
- construction X applied to C([1,34]) ⊂ C([1,28]) [i] based on
- linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2140, 1023, F2, 28) (dual of [1023, 883, 29]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(212, 37, F2, 5) (dual of [37, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(2) [i] 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]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-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(2178, 1061, F2, 34) (dual of [1061, 883, 35]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2180, 1063, F2, 35) (dual of [1063, 883, 36]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2181, 1064, F2, 35) (dual of [1064, 883, 36]-code) | [i] | ||
| 4 | Linear OA(2182, 1065, F2, 35) (dual of [1065, 883, 36]-code) | [i] | ||
| 5 | Linear OOA(2178, 530, F2, 2, 35) (dual of [(530, 2), 882, 36]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2178, 353, F2, 3, 35) (dual of [(353, 3), 881, 36]-NRT-code) | [i] | ||
| 7 | Linear OOA(2178, 265, F2, 4, 35) (dual of [(265, 4), 882, 36]-NRT-code) | [i] | ||
| 8 | Linear OOA(2178, 212, F2, 5, 35) (dual of [(212, 5), 882, 36]-NRT-code) | [i] | ||