Information on Result #1682240
Linear OOA(2155, 779, F2, 7, 27) (dual of [(779, 7), 5298, 28]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2155, 779, F2, 2, 27) (dual of [(779, 2), 1403, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2155, 1042, F2, 2, 27) (dual of [(1042, 2), 1929, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2155, 2084, F2, 27) (dual of [2084, 1929, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2155, 2085, F2, 27) (dual of [2085, 1930, 28]-code), using
- construction XX applied to Ce(26) ⊂ Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2111, 2048, F2, 21) (dual of [2048, 1937, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 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 XX applied to Ce(26) ⊂ Ce(22) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2155, 2085, F2, 27) (dual of [2085, 1930, 28]-code), using
- OOA 2-folding [i] based on linear OA(2155, 2084, F2, 27) (dual of [2084, 1929, 28]-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(2155, 389, F2, 35, 27) (dual of [(389, 35), 13460, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |