Information on Result #1724940
Digital (21, 31, 285)-net over F7, using net defined by OOA based on linear OOA(731, 285, F7, 15, 10) (dual of [(285, 15), 4244, 11]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(731, 571, F7, 3, 10) (dual of [(571, 3), 1682, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(731, 572, F7, 3, 10) (dual of [(572, 3), 1685, 11]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(731, 572, F7, 10) (dual of [572, 541, 11]-code), using
- 218 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 14 times 0, 1, 34 times 0, 1, 64 times 0, 1, 98 times 0) [i] based on linear OA(725, 348, F7, 10) (dual of [348, 323, 11]-code), using
- construction XX applied to C1 = C([341,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([341,8]) [i] based on
- linear OA(722, 342, F7, 9) (dual of [342, 320, 10]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(722, 342, F7, 9) (dual of [342, 320, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(719, 342, F7, 8) (dual of [342, 323, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C([341,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([341,8]) [i] based on
- 218 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 14 times 0, 1, 34 times 0, 1, 64 times 0, 1, 98 times 0) [i] based on linear OA(725, 348, F7, 10) (dual of [348, 323, 11]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(731, 572, F7, 10) (dual of [572, 541, 11]-code), using
- discarding factors / shortening the dual code based on linear OOA(731, 572, F7, 3, 10) (dual of [(572, 3), 1685, 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.