Information on Result #737184

Linear OA(4198, 262216, F4, 27) (dual of [262216, 262018, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,9]) based on
  1. linear OA(4181, 262145, F4, 27) (dual of [262145, 261964, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
  2. linear OA(4127, 262145, F4, 19) (dual of [262145, 262018, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
  3. linear OA(417, 71, F4, 7) (dual of [71, 54, 8]-code), using
    • construction X applied to Ce(6) ⊂ Ce(4) [i] based on
      1. linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
      3. linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(4200, 262218, F4, 27) (dual of [262218, 262018, 28]-code) [i]Code Embedding in Larger Space
2Linear OOA(4198, 131108, F4, 2, 27) (dual of [(131108, 2), 262018, 28]-NRT-code) [i]OOA Folding
3Linear OOA(4198, 87405, F4, 3, 27) (dual of [(87405, 3), 262017, 28]-NRT-code) [i]