Information on Result #694895

Linear OA(27107, 531471, F27, 26) (dual of [531471, 531364, 27]-code), using construction X applied to Ce(25) ⊂ Ce(19) based on
  1. linear OA(27101, 531441, F27, 26) (dual of [531441, 531340, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(2777, 531441, F27, 20) (dual of [531441, 531364, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(27107, 531471, F27, 2, 26) (dual of [(531471, 2), 1062835, 27]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (81, 107, 531471)-net over F27 [i]
3Linear OOA(27107, 265735, F27, 2, 26) (dual of [(265735, 2), 531363, 27]-NRT-code) [i]OOA Folding