Information on Result #1721588
Digital (208, 254, 2055)-net over F4, using net defined by OOA based on linear OOA(4254, 2055, F4, 51, 46) (dual of [(2055, 51), 104551, 47]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] 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
- discarding factors / shortening the dual code based on linear OOA(4254, 16442, F4, 3, 46) (dual of [(16442, 3), 49072, 47]-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.