Information on Result #682000

Linear OA(452, 69, F4, 30) (dual of [69, 17, 31]-code), using construction XX applied to C1 = C([0,80]), C2 = C([1,89]), C3 = C1 + C2 = C([1,80]), and C∩ = C1 ∩ C2 = C([0,89]) based on
  1. linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using contraction [i] based on linear OA(4173, 189, F4, 83) (dual of [189, 16, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,80], and minimum distance d ≥ |{−2,−1,…,80}|+1 = 84 (BCH-bound) [i]
  2. linear OA(449, 63, F4, 29) (dual of [63, 14, 30]-code), using contraction [i] based on linear OA(4175, 189, F4, 89) (dual of [189, 14, 90]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,89], and designed minimum distance d ≥ |I|+1 = 90 [i]
  3. linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using contraction [i] based on linear OA(4176, 189, F4, 92) (dual of [189, 13, 93]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,89], and minimum distance d ≥ |{−2,−1,…,89}|+1 = 93 (BCH-bound) [i]
  4. linear OA(446, 63, F4, 26) (dual of [63, 17, 27]-code), using contraction [i] based on linear OA(4172, 189, F4, 80) (dual of [189, 17, 81]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,80], and designed minimum distance d ≥ |I|+1 = 81 [i]
  5. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-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 OOA(452, 23, F4, 3, 30) (dual of [(23, 3), 17, 31]-NRT-code) [i]OOA Folding