Information on Result #1675202
Linear OOA(2223, 434, F2, 7, 40) (dual of [(434, 7), 2815, 41]-NRT-code), using OOA 2-folding based on linear OOA(2223, 868, F2, 4, 40) (dual of [(868, 4), 3249, 41]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2223, 868, F2, 2, 40) (dual of [(868, 2), 1513, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2223, 1030, F2, 2, 40) (dual of [(1030, 2), 1837, 41]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2222, 1030, F2, 2, 40) (dual of [(1030, 2), 1838, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2222, 2060, F2, 40) (dual of [2060, 1838, 41]-code), using
- strength reduction [i] based on linear OA(2222, 2060, F2, 41) (dual of [2060, 1838, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(38) [i] based on
- linear OA(2221, 2048, F2, 41) (dual of [2048, 1827, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2210, 2048, F2, 39) (dual of [2048, 1838, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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(40) ⊂ Ce(38) [i] based on
- strength reduction [i] based on linear OA(2222, 2060, F2, 41) (dual of [2060, 1838, 42]-code), using
- OOA 2-folding [i] based on linear OA(2222, 2060, F2, 40) (dual of [2060, 1838, 41]-code), using
- 21 times duplication [i] based on linear OOA(2222, 1030, F2, 2, 40) (dual of [(1030, 2), 1838, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2223, 1030, F2, 2, 40) (dual of [(1030, 2), 1837, 41]-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
None.