Information on Result #1453111
Linear OOA(1633, 131084, F16, 2, 8) (dual of [(131084, 2), 262135, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(1633, 131084, F16, 8) (dual of [131084, 131051, 9]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(1632, 131082, F16, 8) (dual of [131082, 131050, 9]-code), using
- trace code [i] based on linear OA(25616, 65541, F256, 8) (dual of [65541, 65525, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(25616, 65541, F256, 8) (dual of [65541, 65525, 9]-code), using
- linear OA(1632, 131083, F16, 7) (dual of [131083, 131051, 8]-code), using Gilbert–Varšamov bound and bm = 1632 > Vbs−1(k−1) = 80246 304169 023850 471583 378724 815956 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(1632, 131082, F16, 8) (dual of [131082, 131050, 9]-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(1633, 65541, F16, 10, 8) (dual of [(65541, 10), 655377, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |