Information on Result #1719916
Digital (177, 205, 37239)-net over F4, using net defined by OOA based on linear OOA(4205, 37239, F4, 33, 28) (dual of [(37239, 33), 1228682, 29]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(4205, 186196, F4, 3, 28) (dual of [(186196, 3), 558383, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4205, 186200, F4, 3, 28) (dual of [(186200, 3), 558395, 29]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4205, 186200, F4, 28) (dual of [186200, 185995, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4205, 262213, F4, 28) (dual of [262213, 262008, 29]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4203, 262211, F4, 28) (dual of [262211, 262008, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(413, 67, F4, 6) (dual of [67, 54, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(413, 64, F4, 6) (dual of [64, 51, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(40, 3, F4, 0) (dual of [3, 3, 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
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(4203, 262211, F4, 28) (dual of [262211, 262008, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4205, 262213, F4, 28) (dual of [262213, 262008, 29]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4205, 186200, F4, 28) (dual of [186200, 185995, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(4205, 186200, F4, 3, 28) (dual of [(186200, 3), 558395, 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.