Information on Result #1718236
Digital (111, 128, 174768)-net over F4, using net defined by OOA based on linear OOA(4128, 174768, F4, 21, 17) (dual of [(174768, 21), 3670000, 18]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(4128, 524305, F4, 3, 17) (dual of [(524305, 3), 1572787, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4128, 524306, F4, 3, 17) (dual of [(524306, 3), 1572790, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4128, 524306, F4, 2, 17) (dual of [(524306, 2), 1048484, 18]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4127, 524306, F4, 2, 17) (dual of [(524306, 2), 1048485, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4127, 1048612, F4, 17) (dual of [1048612, 1048485, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4126, 1048611, F4, 17) (dual of [1048611, 1048485, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4126, 1048611, F4, 17) (dual of [1048611, 1048485, 18]-code), using
- OOA 2-folding [i] based on linear OA(4127, 1048612, F4, 17) (dual of [1048612, 1048485, 18]-code), using
- 41 times duplication [i] based on linear OOA(4127, 524306, F4, 2, 17) (dual of [(524306, 2), 1048485, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4128, 524306, F4, 2, 17) (dual of [(524306, 2), 1048484, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4128, 524306, F4, 3, 17) (dual of [(524306, 3), 1572790, 18]-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.