Information on Result #1684887
Linear OOA(2197, 6416, F2, 7, 26) (dual of [(6416, 7), 44715, 27]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2197, 6416, F2, 5, 26) (dual of [(6416, 5), 31883, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2197, 6556, F2, 5, 26) (dual of [(6556, 5), 32583, 27]-NRT-code), using
- strength reduction [i] based on linear OOA(2197, 6556, F2, 5, 27) (dual of [(6556, 5), 32583, 28]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2197, 32780, F2, 27) (dual of [32780, 32583, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2197, 32784, F2, 27) (dual of [32784, 32587, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2181, 32768, F2, 25) (dual of [32768, 32587, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(2197, 32784, F2, 27) (dual of [32784, 32587, 28]-code), using
- OOA 5-folding [i] based on linear OA(2197, 32780, F2, 27) (dual of [32780, 32583, 28]-code), using
- strength reduction [i] based on linear OOA(2197, 6556, F2, 5, 27) (dual of [(6556, 5), 32583, 28]-NRT-code), using
Mode: 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 OOA(2197, 3207, F2, 35, 26) (dual of [(3207, 35), 112048, 27]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |