Information on Result #1733372
Digital (83, 115, 1057)-net over F9, using net defined by OOA based on linear OOA(9115, 1057, F9, 39, 32) (dual of [(1057, 39), 41108, 33]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OOA(9115, 6343, F9, 3, 32) (dual of [(6343, 3), 18914, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9115, 6348, F9, 3, 32) (dual of [(6348, 3), 18929, 33]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9115, 6348, F9, 32) (dual of [6348, 6233, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(9115, 6572, F9, 32) (dual of [6572, 6457, 33]-code), using
- construction XX applied to Ce(31) ⊂ Ce(29) ⊂ Ce(28) [i] based on
- linear OA(9113, 6561, F9, 32) (dual of [6561, 6448, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(9105, 6561, F9, 30) (dual of [6561, 6456, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(9101, 6561, F9, 29) (dual of [6561, 6460, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(91, 10, F9, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(31) ⊂ Ce(29) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(9115, 6572, F9, 32) (dual of [6572, 6457, 33]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9115, 6348, F9, 32) (dual of [6348, 6233, 33]-code), using
- discarding factors / shortening the dual code based on linear OOA(9115, 6348, F9, 3, 32) (dual of [(6348, 3), 18929, 33]-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.