Information on Result #1718371
Linear OOA(4142, 174771, F4, 21, 18) (dual of [(174771, 21), 3670049, 19]-NRT-code), using OOA 3-folding and stacking with additional row based on linear OOA(4142, 524314, F4, 3, 18) (dual of [(524314, 3), 1572800, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4142, 524314, F4, 2, 18) (dual of [(524314, 2), 1048486, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4142, 1048628, F4, 18) (dual of [1048628, 1048486, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4139, 1048624, F4, 18) (dual of [1048624, 1048485, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4131, 1048576, F4, 18) (dual of [1048576, 1048445, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4139, 1048625, F4, 15) (dual of [1048625, 1048486, 16]-code), using Gilbert–Varšamov bound and bm = 4139 > Vbs−1(k−1) = 106 642560 461792 409923 627689 380487 584874 430228 575430 777377 059074 615722 713981 444427 [i]
- linear OA(42, 3, F4, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), using
- dual of repetition code with length 3 [i]
- linear OA(4139, 1048624, F4, 18) (dual of [1048624, 1048485, 19]-code), using
- construction X with Varšamov bound [i] based on
- OOA 2-folding [i] based on linear OA(4142, 1048628, F4, 18) (dual of [1048628, 1048486, 19]-code), using
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 (124, 142, 174771)-net over F4 | [i] | Net Defined by OOA | |