Information on Result #1197692
Digital (20, 33, 137)-net over F27, using net defined by OOA based on linear OOA(2733, 137, F27, 14, 13) (dual of [(137, 14), 1885, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2733, 412, F27, 2, 13) (dual of [(412, 2), 791, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2733, 414, F27, 2, 13) (dual of [(414, 2), 795, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(278, 48, F27, 2, 6) (dual of [(48, 2), 88, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,89P) [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- linear OOA(2725, 366, F27, 2, 13) (dual of [(366, 2), 707, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2725, 732, F27, 13) (dual of [732, 707, 14]-code), using
- construction XX applied to C1 = C([727,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([727,11]) [i] based on
- linear OA(2723, 728, F27, 12) (dual of [728, 705, 13]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2723, 728, F27, 12) (dual of [728, 705, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2725, 728, F27, 13) (dual of [728, 703, 14]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2721, 728, F27, 11) (dual of [728, 707, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(270, 2, F27, 0) (dual of [2, 2, 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
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([727,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([727,11]) [i] based on
- OOA 2-folding [i] based on linear OA(2725, 732, F27, 13) (dual of [732, 707, 14]-code), using
- linear OOA(278, 48, F27, 2, 6) (dual of [(48, 2), 88, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2733, 414, F27, 2, 13) (dual of [(414, 2), 795, 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.