Information on Result #737170

Linear OA(4207, 1048645, F4, 26) (dual of [1048645, 1048438, 27]-code), using construction X applied to Ce(25) ⊂ Ce(17) based on
  1. linear OA(4191, 1048576, F4, 26) (dual of [1048576, 1048385, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(4131, 1048576, F4, 18) (dual of [1048576, 1048445, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  3. linear OA(416, 69, F4, 7) (dual of [69, 53, 8]-code), using
    • construction XX applied to C1 = C({0,1,2,3,47}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,47}) [i] based on
      1. linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,47}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (BCH-bound) [i]
      2. linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
      3. linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,47}, and minimum distance d ≥ |{−1,0,…,5}|+1 = 8 (BCH-bound) [i]
      4. linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
      5. linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
      6. linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code) (see above)

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(4207, 524322, F4, 2, 26) (dual of [(524322, 2), 1048437, 27]-NRT-code) [i]OOA Folding
2Linear OOA(4207, 349548, F4, 3, 26) (dual of [(349548, 3), 1048437, 27]-NRT-code) [i]
3Linear OOA(4207, 80665, F4, 26, 26) (dual of [(80665, 26), 2097083, 27]-NRT-code) [i]OA Folding and Stacking