Information on Result #672751
Linear OA(2171, 8206, F2, 27) (dual of [8206, 8035, 28]-code), using construction X applied to Ce(26) ⊂ Ce(24) based on
- linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2157, 8192, F2, 25) (dual of [8192, 8035, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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(2171, 8206, F2, 26) (dual of [8206, 8035, 27]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2172, 8207, F2, 27) (dual of [8207, 8035, 28]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2173, 8208, F2, 27) (dual of [8208, 8035, 28]-code) | [i] | ||
| 4 | Linear OA(2174, 8209, F2, 27) (dual of [8209, 8035, 28]-code) | [i] | ||
| 5 | Linear OA(2175, 8210, F2, 27) (dual of [8210, 8035, 28]-code) | [i] | ||
| 6 | Linear OA(2170, 8205, F2, 26) (dual of [8205, 8035, 27]-code) | [i] | Truncation | |
| 7 | Linear OOA(2171, 4103, F2, 2, 27) (dual of [(4103, 2), 8035, 28]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2171, 2735, F2, 3, 27) (dual of [(2735, 3), 8034, 28]-NRT-code) | [i] | ||
| 9 | Linear OOA(2171, 2051, F2, 4, 27) (dual of [(2051, 4), 8033, 28]-NRT-code) | [i] | ||
| 10 | Linear OOA(2171, 1641, F2, 5, 27) (dual of [(1641, 5), 8034, 28]-NRT-code) | [i] | ||
| 11 | Linear OOA(2171, 1367, F2, 6, 27) (dual of [(1367, 6), 8031, 28]-NRT-code) | [i] | ||
| 12 | Linear OOA(2171, 1172, F2, 7, 27) (dual of [(1172, 7), 8033, 28]-NRT-code) | [i] | ||
| 13 | Linear OOA(2171, 1025, F2, 8, 27) (dual of [(1025, 8), 8029, 28]-NRT-code) | [i] | ||
| 14 | Linear OOA(2171, 631, F2, 27, 27) (dual of [(631, 27), 16866, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |