Information on Result #1670256
Linear OOA(2233, 2404, F2, 6, 34) (dual of [(2404, 6), 14191, 35]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2233, 2404, F2, 3, 34) (dual of [(2404, 3), 6979, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2233, 2746, F2, 3, 34) (dual of [(2746, 3), 8005, 35]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2233, 8238, F2, 34) (dual of [8238, 8005, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2233, 8239, F2, 34) (dual of [8239, 8006, 35]-code), using
- 1 times truncation [i] based on linear OA(2234, 8240, F2, 35) (dual of [8240, 8006, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(2222, 8192, F2, 35) (dual of [8192, 7970, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2183, 8192, F2, 29) (dual of [8192, 8009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- 1 times truncation [i] based on linear OA(2234, 8240, F2, 35) (dual of [8240, 8006, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(2233, 8239, F2, 34) (dual of [8239, 8006, 35]-code), using
- OOA 3-folding [i] based on linear OA(2233, 8238, F2, 34) (dual of [8238, 8005, 35]-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2233, 801, F2, 42, 34) (dual of [(801, 42), 33409, 35]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |