Information on Result #677639

Linear OA(374, 90, F3, 44) (dual of [90, 16, 45]-code), using construction XX applied to C1 = C([0,79]), C2 = C([1,87]), C3 = C1 + C2 = C([1,79]), and C∩ = C1 ∩ C2 = C([0,87]) based on
  1. linear OA(365, 80, F3, 40) (dual of [80, 15, 41]-code), using contraction [i] based on linear OA(3145, 160, F3, 81) (dual of [160, 15, 82]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,79], and minimum distance d ≥ |{−1,0,…,79}|+1 = 82 (BCH-bound) [i]
  2. linear OA(369, 80, F3, 43) (dual of [80, 11, 44]-code), using contraction [i] based on linear OA(3149, 160, F3, 87) (dual of [160, 11, 88]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,87], and designed minimum distance d ≥ |I|+1 = 88 [i]
  3. linear OA(370, 80, F3, 44) (dual of [80, 10, 45]-code), using contraction [i] based on linear OA(3150, 160, F3, 89) (dual of [160, 10, 90]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,87], and minimum distance d ≥ |{−1,0,…,87}|+1 = 90 (BCH-bound) [i]
  4. linear OA(364, 80, F3, 39) (dual of [80, 16, 40]-code), using contraction [i] based on linear OA(3144, 160, F3, 79) (dual of [160, 16, 80]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
  5. linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
  6. linear OA(34, 9, F3, 3) (dual of [9, 5, 4]-code or 9-cap in PG(3,3)), 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(374, 90, F3, 43) (dual of [90, 16, 44]-code) [i]Strength Reduction
2Linear OA(374, 90, F3, 42) (dual of [90, 16, 43]-code) [i]
3Linear OA(374, 90, F3, 41) (dual of [90, 16, 42]-code) [i]
4Linear OA(374, 90, F3, 40) (dual of [90, 16, 41]-code) [i]
5Linear OA(374, 90, F3, 39) (dual of [90, 16, 40]-code) [i]
6Linear OA(374, 90, F3, 38) (dual of [90, 16, 39]-code) [i]
7Linear OA(374, 90, F3, 37) (dual of [90, 16, 38]-code) [i]
8Linear OA(376, 92, F3, 44) (dual of [92, 16, 45]-code) [i]Code Embedding in Larger Space
9Linear OA(377, 93, F3, 44) (dual of [93, 16, 45]-code) [i]
10Linear OA(370, 86, F3, 40) (dual of [86, 16, 41]-code) [i]Truncation
11Linear OA(369, 85, F3, 39) (dual of [85, 16, 40]-code) [i]
12Linear OA(368, 84, F3, 38) (dual of [84, 16, 39]-code) [i]
13Linear OA(367, 83, F3, 37) (dual of [83, 16, 38]-code) [i]
14Linear OA(383, 100, F3, 44) (dual of [100, 17, 45]-code) [i]Construction X with VarÅ¡amov Bound
15Linear OOA(374, 45, F3, 2, 44) (dual of [(45, 2), 16, 45]-NRT-code) [i]OOA Folding
16Linear OOA(374, 30, F3, 3, 44) (dual of [(30, 3), 16, 45]-NRT-code) [i]