Information on Result #1704240
Linear OOA(2226, 1960706, F2, 8, 17) (dual of [(1960706, 8), 15685422, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2226, 1960706, F2, 4, 17) (dual of [(1960706, 4), 7842598, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2226, 2097409, F2, 4, 17) (dual of [(2097409, 4), 8389410, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2226, 4194818, F2, 2, 17) (dual of [(4194818, 2), 8389410, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(241, 517, F2, 2, 8) (dual of [(517, 2), 993, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(241, 1034, F2, 8) (dual of [1034, 993, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(241, 1035, F2, 8) (dual of [1035, 994, 9]-code), using
- 1 times truncation [i] based on linear OA(242, 1036, F2, 9) (dual of [1036, 994, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(241, 1024, F2, 9) (dual of [1024, 983, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(231, 1024, F2, 7) (dual of [1024, 993, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(211, 12, F2, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,2)), using
- dual of repetition code with length 12 [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 X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- 1 times truncation [i] based on linear OA(242, 1036, F2, 9) (dual of [1036, 994, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(241, 1035, F2, 8) (dual of [1035, 994, 9]-code), using
- OOA 2-folding [i] based on linear OA(241, 1034, F2, 8) (dual of [1034, 993, 9]-code), using
- linear OOA(2185, 4194301, F2, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2185, 8388602, F2, 17) (dual of [8388602, 8388417, 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 2-folding [i] based on linear OA(2185, 8388602, F2, 17) (dual of [8388602, 8388417, 18]-code), using
- linear OOA(241, 517, F2, 2, 8) (dual of [(517, 2), 993, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA 2-folding [i] based on linear OOA(2226, 4194818, F2, 2, 17) (dual of [(4194818, 2), 8389410, 18]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2226, 1960705, F2, 24, 17) (dual of [(1960705, 24), 47056694, 18]-NRT-code) | [i] | OOA Stacking with Additional Row | |