Information on Result #700738

Linear OA(331, 86, F3, 12) (dual of [86, 55, 13]-code), using construction XX applied to C1 = C({0,1,2,4,5,7,8,53}), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,10,53}) based on
  1. linear OA(329, 80, F3, 11) (dual of [80, 51, 12]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,53}, and minimum distance d ≥ |{−1,0,…,9}|+1 = 12 (BCH-bound) [i]
  2. linear OA(327, 80, F3, 11) (dual of [80, 53, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(331, 80, F3, 12) (dual of [80, 49, 13]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,53}, and minimum distance d ≥ |{−1,0,…,10}|+1 = 13 (BCH-bound) [i]
  4. linear OA(325, 80, F3, 10) (dual of [80, 55, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 11 [i]
  5. linear OA(30, 4, F3, 0) (dual of [4, 4, 1]-code), using
  6. linear OA(30, 2, F3, 0) (dual of [2, 2, 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(336, 100, F3, 12) (dual of [100, 64, 13]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(337, 107, F3, 12) (dual of [107, 70, 13]-code) [i]
3Linear OA(338, 116, F3, 12) (dual of [116, 78, 13]-code) [i]
4Linear OA(339, 127, F3, 12) (dual of [127, 88, 13]-code) [i]
5Linear OOA(331, 43, F3, 2, 12) (dual of [(43, 2), 55, 13]-NRT-code) [i]OOA Folding