Information on Result #1197398
Digital (43, 51, 2230025)-net over F27, using net defined by OOA based on linear OOA(2751, 2230025, F27, 10, 8) (dual of [(2230025, 10), 22300199, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2751, 4460051, F27, 2, 8) (dual of [(4460051, 2), 8920051, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2715, 265750, F27, 2, 4) (dual of [(265750, 2), 531485, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(272, 28, F27, 2, 2) (dual of [(28, 2), 54, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;54,27) [i]
- linear OOA(2713, 265722, F27, 2, 4) (dual of [(265722, 2), 531431, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2713, 531444, F27, 4) (dual of [531444, 531431, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2713, 531445, F27, 4) (dual of [531445, 531432, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(2713, 531441, F27, 4) (dual of [531441, 531428, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(279, 531441, F27, 3) (dual of [531441, 531432, 4]-code or 531441-cap in PG(8,27)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(2713, 531445, F27, 4) (dual of [531445, 531432, 5]-code), using
- OOA 2-folding [i] based on linear OA(2713, 531444, F27, 4) (dual of [531444, 531431, 5]-code), using
- linear OOA(272, 28, F27, 2, 2) (dual of [(28, 2), 54, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2736, 4194301, F27, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2736, 8388602, F27, 8) (dual of [8388602, 8388566, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2736, large, F27, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(2736, large, F27, 8) (dual of [large, large−36, 9]-code), using
- OOA 2-folding [i] based on linear OA(2736, 8388602, F27, 8) (dual of [8388602, 8388566, 9]-code), using
- linear OOA(2715, 265750, F27, 2, 4) (dual of [(265750, 2), 531485, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
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.