Information on Result #672968
Linear OA(2172, 2076, F2, 31) (dual of [2076, 1904, 32]-code), using construction X applied to Ce(30) ⊂ Ce(26) based on
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-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(2172, 2076, F2, 30) (dual of [2076, 1904, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2173, 2077, F2, 31) (dual of [2077, 1904, 32]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2174, 2078, F2, 31) (dual of [2078, 1904, 32]-code) | [i] | ||
| 4 | Linear OA(2175, 2079, F2, 31) (dual of [2079, 1904, 32]-code) | [i] | ||
| 5 | Linear OA(2176, 2080, F2, 31) (dual of [2080, 1904, 32]-code) | [i] | ||
| 6 | Linear OA(2171, 2075, F2, 30) (dual of [2075, 1904, 31]-code) | [i] | Truncation | |
| 7 | Linear OOA(2172, 1038, F2, 2, 31) (dual of [(1038, 2), 1904, 32]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2172, 692, F2, 3, 31) (dual of [(692, 3), 1904, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(2172, 519, F2, 4, 31) (dual of [(519, 4), 1904, 32]-NRT-code) | [i] | ||
| 10 | Linear OOA(2172, 415, F2, 5, 31) (dual of [(415, 5), 1903, 32]-NRT-code) | [i] | ||
| 11 | Linear OOA(2172, 346, F2, 6, 31) (dual of [(346, 6), 1904, 32]-NRT-code) | [i] | ||
| 12 | Linear OOA(2172, 296, F2, 7, 31) (dual of [(296, 7), 1900, 32]-NRT-code) | [i] | ||
| 13 | Linear OOA(2172, 259, F2, 8, 31) (dual of [(259, 8), 1900, 32]-NRT-code) | [i] | ||