Information on Result #1705595
Linear OOA(2242, 2102616, F2, 8, 17) (dual of [(2102616, 8), 16820686, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2242, 2102616, F2, 4, 17) (dual of [(2102616, 4), 8410222, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(257, 5466, F2, 4, 8) (dual of [(5466, 4), 21807, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(257, 5466, F2, 3, 8) (dual of [(5466, 3), 16341, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(257, 16398, F2, 8) (dual of [16398, 16341, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(257, 16399, F2, 8) (dual of [16399, 16342, 9]-code), using
- 1 times truncation [i] based on linear OA(258, 16400, F2, 9) (dual of [16400, 16342, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(257, 16384, F2, 9) (dual of [16384, 16327, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(243, 16384, F2, 7) (dual of [16384, 16341, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(215, 16, F2, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
- dual of repetition code with length 16 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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(258, 16400, F2, 9) (dual of [16400, 16342, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(257, 16399, F2, 8) (dual of [16399, 16342, 9]-code), using
- OOA 3-folding [i] based on linear OA(257, 16398, F2, 8) (dual of [16398, 16341, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(257, 5466, F2, 3, 8) (dual of [(5466, 3), 16341, 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(257, 5466, F2, 4, 8) (dual of [(5466, 4), 21807, 9]-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(2242, 2102615, F2, 24, 17) (dual of [(2102615, 24), 50462518, 18]-NRT-code) | [i] | OOA Stacking with Additional Row | |