Information on Result #675768

Linear OA(3156, 2203, F3, 33) (dual of [2203, 2047, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,15]) based on
  1. linear OA(3155, 2188, F3, 33) (dual of [2188, 2033, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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(31, 15, F3, 1) (dual of [15, 14, 2]-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(3157, 2204, F3, 33) (dual of [2204, 2047, 34]-code) [i]Code Embedding in Larger Space
2Linear OA(3158, 2205, F3, 33) (dual of [2205, 2047, 34]-code) [i]
3Linear OOA(3156, 1480, F3, 2, 33) (dual of [(1480, 2), 2804, 34]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(3156, 1480, F3, 3, 33) (dual of [(1480, 3), 4284, 34]-NRT-code) [i]
5Linear OOA(3156, 1480, F3, 4, 33) (dual of [(1480, 4), 5764, 34]-NRT-code) [i]
6Linear OOA(3156, 1480, F3, 5, 33) (dual of [(1480, 5), 7244, 34]-NRT-code) [i]
7Digital (123, 156, 1480)-net over F3 [i]
8Linear OA(3165, 2228, F3, 33) (dual of [2228, 2063, 34]-code) [i]VarÅ¡amov–Edel Lengthening
9Linear OOA(3156, 1101, F3, 2, 33) (dual of [(1101, 2), 2046, 34]-NRT-code) [i]OOA Folding
10Linear OOA(3156, 734, F3, 3, 33) (dual of [(734, 3), 2046, 34]-NRT-code) [i]
11Linear OOA(3156, 550, F3, 4, 33) (dual of [(550, 4), 2044, 34]-NRT-code) [i]
12Linear OOA(3156, 440, F3, 5, 33) (dual of [(440, 5), 2044, 34]-NRT-code) [i]