Information on Result #700798

Linear OA(382, 98, F3, 47) (dual of [98, 16, 48]-code), using construction XX applied to C1 = C({0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,53}), C2 = C([1,41]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,40,41,53}) based on
  1. linear OA(369, 80, F3, 43) (dual of [80, 11, 44]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,53}, and minimum distance d ≥ |{−3,−2,…,39}|+1 = 44 (BCH-bound) [i]
  2. linear OA(369, 80, F3, 43) (dual of [80, 11, 44]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 44 [i]
  3. linear OA(374, 80, F3, 47) (dual of [80, 6, 48]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,40,41,53}, and minimum distance d ≥ |{1,14,27,…,39}|+1 = 48 (BCH-bound) [i]
  4. linear OA(364, 80, F3, 39) (dual of [80, 16, 40]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 40 [i]
  5. linear OA(34, 9, F3, 3) (dual of [9, 5, 4]-code or 9-cap in PG(3,3)), using
  6. linear OA(34, 9, F3, 3) (dual of [9, 5, 4]-code or 9-cap in PG(3,3)) (see above)

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(381, 97, F3, 46) (dual of [97, 16, 47]-code) [i]Truncation
2Linear OA(378, 94, F3, 43) (dual of [94, 16, 44]-code) [i]
3Linear OA(377, 93, F3, 42) (dual of [93, 16, 43]-code) [i]
4Linear OA(376, 92, F3, 41) (dual of [92, 16, 42]-code) [i]
5Linear OOA(382, 49, F3, 2, 47) (dual of [(49, 2), 16, 48]-NRT-code) [i]OOA Folding