Information on Result #1298866

Linear OA(3174, 59104, F3, 24) (dual of [59104, 58930, 25]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3170, 59099, F3, 24) (dual of [59099, 58929, 25]-code), using
    • construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
      1. linear OA(3161, 59050, F3, 25) (dual of [59050, 58889, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
      2. linear OA(3121, 59050, F3, 19) (dual of [59050, 58929, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
      3. linear OA(39, 49, F3, 4) (dual of [49, 40, 5]-code), using
  2. linear OA(3170, 59100, F3, 20) (dual of [59100, 58930, 21]-code), using Gilbert–VarÅ¡amov bound and bm = 3170 > Vbs−1(k−1) = 19 647663 364515 428307 323077 719525 878234 129146 170108 217591 012313 925788 230854 612155 [i]
  3. linear OA(33, 4, F3, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), 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 OA(3175, 59105, F3, 24) (dual of [59105, 58930, 25]-code) [i]Code Embedding in Larger Space
2Linear OOA(3174, 29552, F3, 2, 24) (dual of [(29552, 2), 58930, 25]-NRT-code) [i]OOA Folding
3Linear OOA(3174, 14776, F3, 4, 24) (dual of [(14776, 4), 58930, 25]-NRT-code) [i]