Information on Result #672867
Linear OA(2187, 4126, F2, 31) (dual of [4126, 3939, 32]-code), using construction X applied to Ce(30) ⊂ Ce(26) based on
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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(2187, 4126, F2, 30) (dual of [4126, 3939, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2188, 4127, F2, 31) (dual of [4127, 3939, 32]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2189, 4128, F2, 31) (dual of [4128, 3939, 32]-code) | [i] | ||
| 4 | Linear OA(2190, 4129, F2, 31) (dual of [4129, 3939, 32]-code) | [i] | ||
| 5 | Linear OA(2191, 4130, F2, 31) (dual of [4130, 3939, 32]-code) | [i] | ||
| 6 | Linear OA(2192, 4131, F2, 31) (dual of [4131, 3939, 32]-code) | [i] | ||
| 7 | Linear OA(2186, 4125, F2, 30) (dual of [4125, 3939, 31]-code) | [i] | Truncation | |
| 8 | Linear OOA(2187, 2063, F2, 2, 31) (dual of [(2063, 2), 3939, 32]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(2187, 1375, F2, 3, 31) (dual of [(1375, 3), 3938, 32]-NRT-code) | [i] | ||
| 10 | Linear OOA(2187, 1031, F2, 4, 31) (dual of [(1031, 4), 3937, 32]-NRT-code) | [i] | ||
| 11 | Linear OOA(2187, 825, F2, 5, 31) (dual of [(825, 5), 3938, 32]-NRT-code) | [i] | ||
| 12 | Linear OOA(2187, 687, F2, 6, 31) (dual of [(687, 6), 3935, 32]-NRT-code) | [i] | ||
| 13 | Linear OOA(2187, 589, F2, 7, 31) (dual of [(589, 7), 3936, 32]-NRT-code) | [i] | ||
| 14 | Linear OOA(2187, 515, F2, 8, 31) (dual of [(515, 8), 3933, 32]-NRT-code) | [i] | ||