Information on Result #1717438
Digital (42, 52, 4318)-net over F4, using net defined by OOA based on linear OOA(452, 4318, F4, 15, 10) (dual of [(4318, 15), 64718, 11]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(452, 8637, F4, 3, 10) (dual of [(8637, 3), 25859, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(452, 8638, F4, 3, 10) (dual of [(8638, 3), 25862, 11]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(452, 8638, F4, 10) (dual of [8638, 8586, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(452, 16394, F4, 10) (dual of [16394, 16342, 11]-code), using
- construction XX applied to Ce(9) ⊂ Ce(8) ⊂ Ce(6) [i] based on
- linear OA(450, 16384, F4, 10) (dual of [16384, 16334, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(443, 16384, F4, 9) (dual of [16384, 16341, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(436, 16384, F4, 7) (dual of [16384, 16348, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(40, 8, F4, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(9) ⊂ Ce(8) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(452, 16394, F4, 10) (dual of [16394, 16342, 11]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(452, 8638, F4, 10) (dual of [8638, 8586, 11]-code), using
- discarding factors / shortening the dual code based on linear OOA(452, 8638, F4, 3, 10) (dual of [(8638, 3), 25862, 11]-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.