Information on Result #672664
Linear OA(2254, 16399, F2, 37) (dual of [16399, 16145, 38]-code), using construction X applied to Ce(36) ⊂ Ce(34) based on
- linear OA(2253, 16384, F2, 37) (dual of [16384, 16131, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(2254, 16399, F2, 36) (dual of [16399, 16145, 37]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2255, 16400, F2, 37) (dual of [16400, 16145, 38]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2256, 16401, F2, 37) (dual of [16401, 16145, 38]-code) | [i] | ||
| 4 | Linear OA(2257, 16402, F2, 37) (dual of [16402, 16145, 38]-code) | [i] | ||
| 5 | Linear OA(2258, 16403, F2, 37) (dual of [16403, 16145, 38]-code) | [i] | ||
| 6 | Linear OA(2253, 16398, F2, 36) (dual of [16398, 16145, 37]-code) | [i] | Truncation | |
| 7 | Linear OOA(2254, 8199, F2, 2, 37) (dual of [(8199, 2), 16144, 38]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2254, 5466, F2, 3, 37) (dual of [(5466, 3), 16144, 38]-NRT-code) | [i] | ||
| 9 | Linear OOA(2254, 4099, F2, 4, 37) (dual of [(4099, 4), 16142, 38]-NRT-code) | [i] | ||
| 10 | Linear OOA(2254, 3279, F2, 5, 37) (dual of [(3279, 5), 16141, 38]-NRT-code) | [i] | ||
| 11 | Linear OOA(2254, 2733, F2, 6, 37) (dual of [(2733, 6), 16144, 38]-NRT-code) | [i] | ||
| 12 | Linear OOA(2254, 2342, F2, 7, 37) (dual of [(2342, 7), 16140, 38]-NRT-code) | [i] | ||
| 13 | Linear OOA(2254, 2049, F2, 8, 37) (dual of [(2049, 8), 16138, 38]-NRT-code) | [i] | ||
| 14 | Linear OOA(2254, 911, F2, 37, 37) (dual of [(911, 37), 33453, 38]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |