Information on Result #1297937

Linear OA(347, 177173, F3, 6) (dual of [177173, 177126, 7]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(346, 177171, F3, 6) (dual of [177171, 177125, 7]-code), using
    • construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
      1. linear OA(345, 177147, F3, 7) (dual of [177147, 177102, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(323, 177147, F3, 4) (dual of [177147, 177124, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
      3. linear OA(323, 24, F3, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
      4. linear OA(31, 24, F3, 1) (dual of [24, 23, 2]-code), using
  2. linear OA(346, 177172, F3, 5) (dual of [177172, 177126, 6]-code), using Gilbert–VarÅ¡amov bound and bm = 346 > Vbs−1(k−1) = 656 854956 953745 793883 [i]
  3. linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using

Mode: 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(347, 177173, F3, 2, 6) (dual of [(177173, 2), 354299, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(347, 177173, F3, 3, 6) (dual of [(177173, 3), 531472, 7]-NRT-code) [i]
3Linear OOA(347, 177173, F3, 4, 6) (dual of [(177173, 4), 708645, 7]-NRT-code) [i]
4Linear OOA(347, 177173, F3, 5, 6) (dual of [(177173, 5), 885818, 7]-NRT-code) [i]