Information on Result #1197776
Digital (72, 85, 1486683)-net over F27, using net defined by OOA based on linear OOA(2785, 1486683, F27, 14, 13) (dual of [(1486683, 14), 20813477, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2785, 4460050, F27, 2, 13) (dual of [(4460050, 2), 8920015, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2785, 4460051, F27, 2, 13) (dual of [(4460051, 2), 8920017, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2724, 265750, F27, 2, 6) (dual of [(265750, 2), 531476, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(273, 28, F27, 2, 3) (dual of [(28, 2), 53, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;53,27) [i]
- linear OOA(2721, 265722, F27, 2, 6) (dual of [(265722, 2), 531423, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2721, 531444, F27, 6) (dual of [531444, 531423, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(2721, 531445, F27, 6) (dual of [531445, 531424, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(2721, 531441, F27, 6) (dual of [531441, 531420, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2717, 531441, F27, 5) (dual of [531441, 531424, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(2721, 531445, F27, 6) (dual of [531445, 531424, 7]-code), using
- OOA 2-folding [i] based on linear OA(2721, 531444, F27, 6) (dual of [531444, 531423, 7]-code), using
- linear OOA(273, 28, F27, 2, 3) (dual of [(28, 2), 53, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2761, 4194301, F27, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2761, 8388602, F27, 13) (dual of [8388602, 8388541, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- OOA 2-folding [i] based on linear OA(2761, 8388602, F27, 13) (dual of [8388602, 8388541, 14]-code), using
- linear OOA(2724, 265750, F27, 2, 6) (dual of [(265750, 2), 531476, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2785, 4460051, F27, 2, 13) (dual of [(4460051, 2), 8920017, 14]-NRT-code), using
Mode: Constructive and 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.