Information on Result #731761

Linear OA(4134, 142, F4, 93) (dual of [142, 8, 94]-code), using juxtaposition based on
  1. linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using
    • the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
  2. linear OA(469, 77, F4, 49) (dual of [77, 8, 50]-code), using
    • construction X applied to C([0,25]) ⊂ C([0,21]) [i] based on
      1. linear OA(463, 65, F4, 51) (dual of [65, 2, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,25], and minimum distance d ≥ |{−15,−4,7,…,15}|+1 = 52 (BCH-bound) [i]
      2. linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
      3. linear OA(46, 12, F4, 5) (dual of [12, 6, 6]-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(4134, 142, F4, 92) (dual of [142, 8, 93]-code) [i]Strength Reduction
2Linear OA(4134, 142, F4, 91) (dual of [142, 8, 92]-code) [i]
3Linear OOA(4134, 71, F4, 2, 93) (dual of [(71, 2), 8, 94]-NRT-code) [i]OOA Folding