Information on Result #1729712
Digital (134, 164, 52436)-net over F8, using net defined by OOA based on linear OOA(8164, 52436, F8, 33, 30) (dual of [(52436, 33), 1730224, 31]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8164, 262181, F8, 3, 30) (dual of [(262181, 3), 786379, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8164, 262182, F8, 3, 30) (dual of [(262182, 3), 786382, 31]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8164, 262182, F8, 30) (dual of [262182, 262018, 31]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8163, 262180, F8, 30) (dual of [262180, 262017, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(8157, 262144, F8, 30) (dual of [262144, 261987, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(86, 36, F8, 4) (dual of [36, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(8163, 262181, F8, 29) (dual of [262181, 262018, 30]-code), using Gilbert–Varšamov bound and bm = 8163 > Vbs−1(k−1) = 79 208613 456124 726007 723702 911765 748373 906861 775586 397681 248136 821173 319858 715584 197721 624928 115251 040669 124668 682055 246236 630910 042747 801255 505832 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(8163, 262180, F8, 30) (dual of [262180, 262017, 31]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8164, 262182, F8, 30) (dual of [262182, 262018, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(8164, 262182, F8, 3, 30) (dual of [(262182, 3), 786382, 31]-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.