Information on Result #1719883
Linear OOA(4186, 13120, F4, 33, 28) (dual of [(13120, 33), 432774, 29]-NRT-code), using OOA 5-folding and stacking with additional row based on linear OOA(4186, 65601, F4, 3, 28) (dual of [(65601, 3), 196617, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4186, 65604, F4, 3, 28) (dual of [(65604, 3), 196626, 29]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4186, 65604, F4, 28) (dual of [65604, 65418, 29]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4182, 65597, F4, 28) (dual of [65597, 65415, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4182, 65600, F4, 26) (dual of [65600, 65418, 27]-code), using Gilbert–Varšamov bound and bm = 4182 > Vbs−1(k−1) = 143841 756290 016350 169662 786892 659721 213183 918115 845900 235006 828617 848740 709183 661310 225110 542099 256145 980430 [i]
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(4182, 65597, F4, 28) (dual of [65597, 65415, 29]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4186, 65604, F4, 28) (dual of [65604, 65418, 29]-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 (158, 186, 13120)-net over F4 | [i] | Net Defined by OOA | |