Information on Result #1711226
Digital (144, 172, 628)-net over F2, using net defined by OOA based on linear OOA(2172, 628, F2, 35, 28) (dual of [(628, 35), 21808, 29]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2172, 1257, F2, 7, 28) (dual of [(1257, 7), 8627, 29]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2172, 1257, F2, 3, 28) (dual of [(1257, 3), 3599, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2172, 1370, F2, 3, 28) (dual of [(1370, 3), 3938, 29]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2171, 1370, F2, 3, 28) (dual of [(1370, 3), 3939, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2171, 4110, F2, 28) (dual of [4110, 3939, 29]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2169, 4108, F2, 28) (dual of [4108, 3939, 29]-code), using
- 1 times truncation [i] based on linear OA(2170, 4109, F2, 29) (dual of [4109, 3939, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2169, 4096, F2, 29) (dual of [4096, 3927, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(28) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2170, 4109, F2, 29) (dual of [4109, 3939, 30]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2169, 4108, F2, 28) (dual of [4108, 3939, 29]-code), using
- OOA 3-folding [i] based on linear OA(2171, 4110, F2, 28) (dual of [4110, 3939, 29]-code), using
- 21 times duplication [i] based on linear OOA(2171, 1370, F2, 3, 28) (dual of [(1370, 3), 3939, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2172, 1370, F2, 3, 28) (dual of [(1370, 3), 3938, 29]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2172, 1257, F2, 3, 28) (dual of [(1257, 3), 3599, 29]-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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.