Information on Result #681987

Linear OA(443, 70, F4, 23) (dual of [70, 27, 24]-code), using construction XX applied to C([0,68]) ⊂ C([0,62]) ⊂ C([1,62]) based on
  1. linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using contraction [i] based on linear OA(4167, 189, F4, 71) (dual of [189, 22, 72]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,68], and minimum distance d ≥ |{−2,−1,…,68}|+1 = 72 (BCH-bound) [i]
  2. linear OA(437, 63, F4, 21) (dual of [63, 26, 22]-code), using contraction [i] based on linear OA(4163, 189, F4, 65) (dual of [189, 26, 66]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,62], and minimum distance d ≥ |{−2,−1,…,62}|+1 = 66 (BCH-bound) [i]
  3. linear OA(436, 63, F4, 20) (dual of [63, 27, 21]-code), using contraction [i] based on linear OA(4162, 189, F4, 62) (dual of [189, 27, 63]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [i]
  4. linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code), using
  5. linear OA(40, 1, F4, 0) (dual of [1, 1, 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(443, 70, F4, 22) (dual of [70, 27, 23]-code) [i]Strength Reduction
2Linear OA(441, 68, F4, 21) (dual of [68, 27, 22]-code) [i]Truncation
3Linear OA(440, 67, F4, 20) (dual of [67, 27, 21]-code) [i]
4Linear OA(439, 66, F4, 19) (dual of [66, 27, 20]-code) [i]
5Linear OOA(443, 35, F4, 2, 23) (dual of [(35, 2), 27, 24]-NRT-code) [i]OOA Folding