Information on Result #701085

Linear OA(456, 78, F4, 30) (dual of [78, 22, 31]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,31,47}), C2 = C([0,23]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,47}) based on
  1. linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,31,47}, and minimum distance d ≥ |{−4,−3,…,22}|+1 = 28 (BCH-bound) [i]
  2. linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 27 [i]
  3. linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,31,47}, and minimum distance d ≥ |{−4,−3,…,25}|+1 = 31 (BCH-bound) [i]
  4. linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
  5. linear OA(44, 10, F4, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,4)), using
  6. linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), 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(455, 77, F4, 29) (dual of [77, 22, 30]-code) [i]Truncation
2Linear OOA(456, 39, F4, 2, 30) (dual of [(39, 2), 22, 31]-NRT-code) [i]OOA Folding
3Linear OOA(456, 26, F4, 3, 30) (dual of [(26, 3), 22, 31]-NRT-code) [i]