Information on Result #737041

Linear OA(3123, 2226, F3, 25) (dual of [2226, 2103, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,9]) based on
  1. linear OA(3113, 2188, F3, 25) (dual of [2188, 2075, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
  2. linear OA(385, 2188, F3, 19) (dual of [2188, 2103, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(3123, 2226, F3, 24) (dual of [2226, 2103, 25]-code) [i]Strength Reduction
2Linear OA(3125, 2228, F3, 25) (dual of [2228, 2103, 26]-code) [i]Code Embedding in Larger Space
3Linear OA(3126, 2229, F3, 25) (dual of [2229, 2103, 26]-code) [i]
4Linear OA(3127, 2230, F3, 25) (dual of [2230, 2103, 26]-code) [i]
5Linear OA(3128, 2231, F3, 25) (dual of [2231, 2103, 26]-code) [i]
6Linear OA(3122, 2225, F3, 24) (dual of [2225, 2103, 25]-code) [i]Truncation
7Linear OA(3126, 2230, F3, 25) (dual of [2230, 2104, 26]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OA(3127, 2232, F3, 25) (dual of [2232, 2105, 26]-code) [i]
9Linear OOA(3123, 1113, F3, 2, 25) (dual of [(1113, 2), 2103, 26]-NRT-code) [i]OOA Folding
10Linear OOA(3123, 742, F3, 3, 25) (dual of [(742, 3), 2103, 26]-NRT-code) [i]
11Linear OOA(3123, 445, F3, 5, 25) (dual of [(445, 5), 2102, 26]-NRT-code) [i]