Information on Result #1299600

Linear OA(3237, 6607, F3, 42) (dual of [6607, 6370, 43]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3233, 6602, F3, 42) (dual of [6602, 6369, 43]-code), using
    • construction X applied to C([0,21]) ⊂ C([0,18]) [i] based on
      1. linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
      2. linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
      3. linear OA(38, 40, F3, 4) (dual of [40, 32, 5]-code), using
  2. linear OA(3233, 6603, F3, 38) (dual of [6603, 6370, 39]-code), using Gilbert–VarÅ¡amov bound and bm = 3233 > Vbs−1(k−1) = 19 261962 626123 021381 245112 919150 301814 699453 228446 961010 260547 580979 472108 117298 926487 333230 485815 607079 807401 [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(3238, 6608, F3, 42) (dual of [6608, 6370, 43]-code) [i]Code Embedding in Larger Space