Information on Result #1721587
Linear OOA(4254, 2055, F4, 51, 46) (dual of [(2055, 51), 104551, 47]-NRT-code), using OOA 8-folding and stacking with additional row based on linear OOA(4254, 16441, F4, 3, 46) (dual of [(16441, 3), 49069, 47]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4254, 16442, F4, 3, 46) (dual of [(16442, 3), 49072, 47]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4254, 16442, F4, 46) (dual of [16442, 16188, 47]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4253, 16440, F4, 46) (dual of [16440, 16187, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(37) [i] based on
- linear OA(4239, 16384, F4, 46) (dual of [16384, 16145, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(4197, 16384, F4, 38) (dual of [16384, 16187, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to Ce(45) ⊂ Ce(37) [i] based on
- linear OA(4253, 16441, F4, 45) (dual of [16441, 16188, 46]-code), using Gilbert–Varšamov bound and bm = 4253 > Vbs−1(k−1) = 110 609333 782011 556837 462355 978892 871974 061775 726667 881821 225847 938068 072305 225392 178123 242930 701054 057013 957173 110224 821398 319778 035081 229098 500844 144538 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(4253, 16440, F4, 46) (dual of [16440, 16187, 47]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4254, 16442, F4, 46) (dual of [16442, 16188, 47]-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 (208, 254, 2055)-net over F4 | [i] | Net Defined by OOA | |