Information on Result #672594
Linear OA(2152, 32784, F2, 21) (dual of [32784, 32632, 22]-code), using construction X applied to Ce(20) ⊂ Ce(18) based on
- linear OA(2151, 32768, F2, 21) (dual of [32768, 32617, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2136, 32768, F2, 19) (dual of [32768, 32632, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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(2152, 32784, F2, 20) (dual of [32784, 32632, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2153, 32785, F2, 21) (dual of [32785, 32632, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2154, 32786, F2, 21) (dual of [32786, 32632, 22]-code) | [i] | ||
| 4 | Linear OA(2155, 32787, F2, 21) (dual of [32787, 32632, 22]-code) | [i] | ||
| 5 | Linear OA(2156, 32788, F2, 21) (dual of [32788, 32632, 22]-code) | [i] | ||
| 6 | Linear OA(2151, 32783, F2, 20) (dual of [32783, 32632, 21]-code) | [i] | Truncation | |
| 7 | Linear OOA(2152, 16392, F2, 2, 21) (dual of [(16392, 2), 32632, 22]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2152, 10928, F2, 3, 21) (dual of [(10928, 3), 32632, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(2152, 8196, F2, 4, 21) (dual of [(8196, 4), 32632, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(2152, 6556, F2, 5, 21) (dual of [(6556, 5), 32628, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(2152, 5464, F2, 6, 21) (dual of [(5464, 6), 32632, 22]-NRT-code) | [i] | ||
| 12 | Linear OOA(2152, 4683, F2, 7, 21) (dual of [(4683, 7), 32629, 22]-NRT-code) | [i] | ||
| 13 | Linear OOA(2152, 4098, F2, 8, 21) (dual of [(4098, 8), 32632, 22]-NRT-code) | [i] | ||
| 14 | Linear OOA(2152, 3278, F2, 21, 21) (dual of [(3278, 21), 68686, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |