Information on Result #1716338
Digital (178, 209, 6564)-net over F3, using net defined by OOA based on linear OOA(3209, 6564, F3, 35, 31) (dual of [(6564, 35), 229531, 32]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3209, 19693, F3, 5, 31) (dual of [(19693, 5), 98256, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3209, 19695, F3, 5, 31) (dual of [(19695, 5), 98266, 32]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3209, 19695, F3, 3, 31) (dual of [(19695, 3), 58876, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3209, 59085, F3, 31) (dual of [59085, 58876, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3209, 59087, F3, 31) (dual of [59087, 58878, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(38, 38, F3, 4) (dual of [38, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3209, 59087, F3, 31) (dual of [59087, 58878, 32]-code), using
- OOA 3-folding [i] based on linear OA(3209, 59085, F3, 31) (dual of [59085, 58876, 32]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3209, 19695, F3, 3, 31) (dual of [(19695, 3), 58876, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3209, 19695, F3, 5, 31) (dual of [(19695, 5), 98266, 32]-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.