Information on Result #672678
Linear OA(2128, 16399, F2, 19) (dual of [16399, 16271, 20]-code), using construction X applied to Ce(18) ⊂ Ce(16) based on
- linear OA(2127, 16384, F2, 19) (dual of [16384, 16257, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2113, 16384, F2, 17) (dual of [16384, 16271, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(2128, 16399, F2, 18) (dual of [16399, 16271, 19]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2129, 16400, F2, 19) (dual of [16400, 16271, 20]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2130, 16401, F2, 19) (dual of [16401, 16271, 20]-code) | [i] | ||
| 4 | Linear OA(2131, 16402, F2, 19) (dual of [16402, 16271, 20]-code) | [i] | ||
| 5 | Linear OA(2132, 16403, F2, 19) (dual of [16403, 16271, 20]-code) | [i] | ||
| 6 | Linear OA(2127, 16398, F2, 18) (dual of [16398, 16271, 19]-code) | [i] | Truncation | |
| 7 | Linear OOA(2128, 8199, F2, 2, 19) (dual of [(8199, 2), 16270, 20]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2128, 5466, F2, 3, 19) (dual of [(5466, 3), 16270, 20]-NRT-code) | [i] | ||
| 9 | Linear OOA(2128, 4099, F2, 4, 19) (dual of [(4099, 4), 16268, 20]-NRT-code) | [i] | ||
| 10 | Linear OOA(2128, 3279, F2, 5, 19) (dual of [(3279, 5), 16267, 20]-NRT-code) | [i] | ||
| 11 | Linear OOA(2128, 2733, F2, 6, 19) (dual of [(2733, 6), 16270, 20]-NRT-code) | [i] | ||
| 12 | Linear OOA(2128, 2342, F2, 7, 19) (dual of [(2342, 7), 16266, 20]-NRT-code) | [i] | ||
| 13 | Linear OOA(2128, 2049, F2, 8, 19) (dual of [(2049, 8), 16264, 20]-NRT-code) | [i] | ||
| 14 | Linear OOA(2128, 1822, F2, 19, 19) (dual of [(1822, 19), 34490, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |