Information on Result #677506

Linear OA(3178, 198, F3, 98) (dual of [198, 20, 99]-code), using construction XX applied to Ce(97) ⊂ Ce(91) ⊂ Ce(90) based on
  1. linear OA(3170, 183, F3, 98) (dual of [183, 13, 99]-code), using an extension Ce(97) of the narrow-sense BCH-code C(I) with length 182 | 36−1, defining interval I = [1,97], and designed minimum distance d ≥ |I|+1 = 98 [i]
  2. linear OA(3164, 183, F3, 92) (dual of [183, 19, 93]-code), using an extension Ce(91) of the narrow-sense BCH-code C(I) with length 182 | 36−1, defining interval I = [1,91], and designed minimum distance d ≥ |I|+1 = 92 [i]
  3. linear OA(3163, 183, F3, 91) (dual of [183, 20, 92]-code), using an extension Ce(90) of the narrow-sense BCH-code C(I) with length 182 | 36−1, defining interval I = [1,90], and designed minimum distance d ≥ |I|+1 = 91 [i]
  4. linear OA(37, 14, F3, 5) (dual of [14, 7, 6]-code), using
  5. linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(3178, 198, F3, 97) (dual of [198, 20, 98]-code) [i]Strength Reduction
2Linear OA(3178, 198, F3, 96) (dual of [198, 20, 97]-code) [i]
3Linear OA(3179, 199, F3, 98) (dual of [199, 20, 99]-code) [i]Code Embedding in Larger Space
4Linear OA(3181, 201, F3, 98) (dual of [201, 20, 99]-code) [i]
5Linear OA(3182, 202, F3, 98) (dual of [202, 20, 99]-code) [i]
6Linear OA(3176, 196, F3, 96) (dual of [196, 20, 97]-code) [i]Truncation
7Linear OA(3175, 195, F3, 95) (dual of [195, 20, 96]-code) [i]
8Linear OA(3170, 190, F3, 90) (dual of [190, 20, 91]-code) [i]
9Linear OOA(3178, 99, F3, 2, 98) (dual of [(99, 2), 20, 99]-NRT-code) [i]OOA Folding
10Linear OOA(3178, 66, F3, 3, 98) (dual of [(66, 3), 20, 99]-NRT-code) [i]