Information on Result #672669
Linear OA(2212, 16399, F2, 31) (dual of [16399, 16187, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2197, 16384, F2, 29) (dual of [16384, 16187, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(2212, 16399, F2, 30) (dual of [16399, 16187, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2213, 16400, F2, 31) (dual of [16400, 16187, 32]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2214, 16401, F2, 31) (dual of [16401, 16187, 32]-code) | [i] | ||
| 4 | Linear OA(2215, 16402, F2, 31) (dual of [16402, 16187, 32]-code) | [i] | ||
| 5 | Linear OA(2216, 16403, F2, 31) (dual of [16403, 16187, 32]-code) | [i] | ||
| 6 | Linear OA(2211, 16398, F2, 30) (dual of [16398, 16187, 31]-code) | [i] | Truncation | |
| 7 | Linear OOA(2212, 8199, F2, 2, 31) (dual of [(8199, 2), 16186, 32]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2212, 5466, F2, 3, 31) (dual of [(5466, 3), 16186, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(2212, 4099, F2, 4, 31) (dual of [(4099, 4), 16184, 32]-NRT-code) | [i] | ||
| 10 | Linear OOA(2212, 3279, F2, 5, 31) (dual of [(3279, 5), 16183, 32]-NRT-code) | [i] | ||
| 11 | Linear OOA(2212, 2733, F2, 6, 31) (dual of [(2733, 6), 16186, 32]-NRT-code) | [i] | ||
| 12 | Linear OOA(2212, 2342, F2, 7, 31) (dual of [(2342, 7), 16182, 32]-NRT-code) | [i] | ||
| 13 | Linear OOA(2212, 2049, F2, 8, 31) (dual of [(2049, 8), 16180, 32]-NRT-code) | [i] | ||
| 14 | Linear OOA(2212, 1093, F2, 31, 31) (dual of [(1093, 31), 33671, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |