Information on Result #701109

Linear OA(459, 75, F4, 32) (dual of [75, 16, 33]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,31,47}), C2 = C([0,27]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,31,47}) based on
  1. linear OA(453, 63, F4, 31) (dual of [63, 10, 32]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,31,47}, and minimum distance d ≥ |{−4,−3,…,26}|+1 = 32 (BCH-bound) [i]
  2. linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 31 [i]
  3. linear OA(456, 63, F4, 34) (dual of [63, 7, 35]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,31,47}, and minimum distance d ≥ |{−4,−3,…,29}|+1 = 35 (BCH-bound) [i]
  4. linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
  5. linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-code), 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(2187, 207, F2, 65) (dual of [207, 20, 66]-code) [i]Concatenation of Two Codes
2Linear OOA(459, 25, F4, 3, 32) (dual of [(25, 3), 16, 33]-NRT-code) [i]OOA Folding