Information on Result #700750
Linear OA(345, 99, F3, 16) (dual of [99, 54, 17]-code), using construction XX applied to C1 = C({0,1,2,4,5,7,8,10,26,53}), C2 = C([1,11]), C3 = C1 + C2 = C([1,10]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,10,11,26,53}) based on
- linear OA(335, 80, F3, 14) (dual of [80, 45, 15]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,26,53}, and minimum distance d ≥ |{−3,−2,…,10}|+1 = 15 (BCH-bound) [i]
- linear OA(330, 80, F3, 12) (dual of [80, 50, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(339, 80, F3, 16) (dual of [80, 41, 17]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,11,26,53}, and minimum distance d ≥ |{−3,−2,…,12}|+1 = 17 (BCH-bound) [i]
- linear OA(326, 80, F3, 10) (dual of [80, 54, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(35, 14, F3, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,3)), using
- linear OA(31, 5, F3, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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
None.