Information on Result #674750

Linear OA(3141, 177188, F3, 19) (dual of [177188, 177047, 20]-code), using construction X applied to Ce(18) ⊂ Ce(13) based on
  1. linear OA(3133, 177147, F3, 19) (dual of [177147, 177014, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(3100, 177147, F3, 14) (dual of [177147, 177047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
  3. linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
    • the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]

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(3142, 177189, F3, 19) (dual of [177189, 177047, 20]-code) [i]Code Embedding in Larger Space
2Linear OA(3143, 177190, F3, 19) (dual of [177190, 177047, 20]-code) [i]
3Linear OA(3140, 177187, F3, 18) (dual of [177187, 177047, 19]-code) [i]Truncation
4Linear OOA(3141, 88594, F3, 2, 19) (dual of [(88594, 2), 177047, 20]-NRT-code) [i]OOA Folding
5Linear OOA(3141, 59062, F3, 3, 19) (dual of [(59062, 3), 177045, 20]-NRT-code) [i]
6Linear OOA(3141, 44297, F3, 4, 19) (dual of [(44297, 4), 177047, 20]-NRT-code) [i]
7Linear OOA(3141, 35437, F3, 5, 19) (dual of [(35437, 5), 177044, 20]-NRT-code) [i]
8Linear OOA(3141, 19687, F3, 19, 19) (dual of [(19687, 19), 373912, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row