Information on Result #1720076
Digital (191, 220, 78563)-net over F4, using net defined by OOA based on linear OOA(4220, 78563, F4, 33, 29) (dual of [(78563, 33), 2592359, 30]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(4220, 392816, F4, 3, 29) (dual of [(392816, 3), 1178228, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4220, 392817, F4, 3, 29) (dual of [(392817, 3), 1178231, 30]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4220, 392817, F4, 2, 29) (dual of [(392817, 2), 785414, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4220, 524307, F4, 2, 29) (dual of [(524307, 2), 1048394, 30]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4219, 524307, F4, 2, 29) (dual of [(524307, 2), 1048395, 30]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4217, 524306, F4, 2, 29) (dual of [(524306, 2), 1048395, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4217, 1048612, F4, 29) (dual of [1048612, 1048395, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4216, 1048611, F4, 29) (dual of [1048611, 1048395, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4181, 1048576, F4, 25) (dual of [1048576, 1048395, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4216, 1048611, F4, 29) (dual of [1048611, 1048395, 30]-code), using
- OOA 2-folding [i] based on linear OA(4217, 1048612, F4, 29) (dual of [1048612, 1048395, 30]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4217, 524306, F4, 2, 29) (dual of [(524306, 2), 1048395, 30]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4219, 524307, F4, 2, 29) (dual of [(524307, 2), 1048395, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4220, 524307, F4, 2, 29) (dual of [(524307, 2), 1048394, 30]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4220, 392817, F4, 2, 29) (dual of [(392817, 2), 785414, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4220, 392817, F4, 3, 29) (dual of [(392817, 3), 1178231, 30]-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.