Information on Result #679249

Linear OA(4173, 16448, F4, 30) (dual of [16448, 16275, 31]-code), using construction X applied to Ce(29) ⊂ Ce(20) based on
  1. linear OA(4155, 16384, F4, 30) (dual of [16384, 16229, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
  2. linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  3. linear OA(418, 64, F4, 8) (dual of [64, 46, 9]-code), using
    • 1 times truncation [i] based on linear OA(419, 65, F4, 9) (dual of [65, 46, 10]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]

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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(4173, 8224, F4, 2, 30) (dual of [(8224, 2), 16275, 31]-NRT-code) [i]OOA Folding
2Linear OOA(4173, 5482, F4, 3, 30) (dual of [(5482, 3), 16273, 31]-NRT-code) [i]