Information on Result #694755

Linear OA(2787, 531472, F27, 21) (dual of [531472, 531385, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,7]) based on
  1. linear OA(2781, 531442, F27, 21) (dual of [531442, 531361, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  2. linear OA(2757, 531442, F27, 15) (dual of [531442, 531385, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
  3. linear OA(276, 30, F27, 5) (dual of [30, 24, 6]-code), using
    • construction X applied to C([0,2]) ⊂ C([1,2]) [i] based on
      1. linear OA(275, 28, F27, 5) (dual of [28, 23, 6]-code or 28-arc in PG(4,27)), using the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
      2. linear OA(274, 28, F27, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,27)), using the narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [1,2], and minimum distance d ≥ |{1,2}| + |{−3,0}| = 4 (simple Roos-bound) [i]
      3. linear OA(271, 2, F27, 1) (dual of [2, 1, 2]-code), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(2787, 265736, F27, 2, 21) (dual of [(265736, 2), 531385, 22]-NRT-code) [i]OOA Folding
2Linear OOA(2787, 53147, F27, 21, 21) (dual of [(53147, 21), 1116000, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row