Information on Result #737037

Linear OA(3179, 2226, F3, 37) (dual of [2226, 2047, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,15]) based on
  1. linear OA(3169, 2188, F3, 37) (dual of [2188, 2019, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
  2. linear OA(3141, 2188, F3, 31) (dual of [2188, 2047, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
  3. linear OA(310, 38, F3, 5) (dual of [38, 28, 6]-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 OA(3179, 2226, F3, 36) (dual of [2226, 2047, 37]-code) [i]Strength Reduction
2Linear OA(3181, 2228, F3, 37) (dual of [2228, 2047, 38]-code) [i]Code Embedding in Larger Space
3Linear OA(3182, 2229, F3, 37) (dual of [2229, 2047, 38]-code) [i]
4Linear OA(3183, 2230, F3, 37) (dual of [2230, 2047, 38]-code) [i]
5Linear OA(3184, 2231, F3, 37) (dual of [2231, 2047, 38]-code) [i]
6Linear OA(3178, 2225, F3, 36) (dual of [2225, 2047, 37]-code) [i]Truncation
7Linear OA(3182, 2230, F3, 37) (dual of [2230, 2048, 38]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OA(3183, 2232, F3, 37) (dual of [2232, 2049, 38]-code) [i]
9Linear OOA(3179, 1113, F3, 2, 37) (dual of [(1113, 2), 2047, 38]-NRT-code) [i]OOA Folding
10Linear OOA(3179, 742, F3, 3, 37) (dual of [(742, 3), 2047, 38]-NRT-code) [i]
11Linear OOA(3179, 445, F3, 5, 37) (dual of [(445, 5), 2046, 38]-NRT-code) [i]