Information on Result #1710217
Linear OOA(2231, 2098179, F2, 24, 17) (dual of [(2098179, 24), 50356065, 18]-NRT-code), using OOA stacking with additional row based on linear OOA(2231, 2098180, F2, 8, 17) (dual of [(2098180, 8), 16785209, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2231, 2098180, F2, 4, 17) (dual of [(2098180, 4), 8392489, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(246, 1030, F2, 4, 8) (dual of [(1030, 4), 4074, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(246, 1030, F2, 2, 8) (dual of [(1030, 2), 2014, 9]-NRT-code), using
- strength reduction [i] based on linear OOA(246, 1030, F2, 2, 9) (dual of [(1030, 2), 2014, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(246, 2060, F2, 9) (dual of [2060, 2014, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(245, 2048, F2, 9) (dual of [2048, 2003, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(234, 2048, F2, 7) (dual of [2048, 2014, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(8) ⊂ Ce(6) [i] based on
- OOA 2-folding [i] based on linear OA(246, 2060, F2, 9) (dual of [2060, 2014, 10]-code), using
- strength reduction [i] based on linear OOA(246, 1030, F2, 2, 9) (dual of [(1030, 2), 2014, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(246, 1030, F2, 2, 8) (dual of [(1030, 2), 2014, 9]-NRT-code), using
- linear OOA(2185, 2097150, F2, 4, 17) (dual of [(2097150, 4), 8388415, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 4-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- linear OOA(246, 1030, F2, 4, 8) (dual of [(1030, 4), 4074, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
Mode: Linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
Result | This result only | Method | ||
---|---|---|---|---|
1 | Digital (214, 231, 2098179)-net over F2 | [i] | Net Defined by OOA |