Information on Result #737163

Linear OA(4247, 1048645, F4, 31) (dual of [1048645, 1048398, 32]-code), using construction X applied to Ce(30) ⊂ Ce(22) based on
  1. linear OA(4231, 1048576, F4, 31) (dual of [1048576, 1048345, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(4247, 524322, F4, 2, 31) (dual of [(524322, 2), 1048397, 32]-NRT-code) [i]OOA Folding
2Linear OOA(4247, 349548, F4, 3, 31) (dual of [(349548, 3), 1048397, 32]-NRT-code) [i]