Information on Result #711970

Linear OA(5129, 656, F5, 38) (dual of [656, 527, 39]-code), using construction XX applied to C1 = C([618,30]), C2 = C([1,31]), C3 = C1 + C2 = C([1,30]), and C∩ = C1 ∩ C2 = C([618,31]) based on
  1. linear OA(5115, 624, F5, 37) (dual of [624, 509, 38]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−6,−5,…,30}, and designed minimum distance d ≥ |I|+1 = 38 [i]
  2. linear OA(598, 624, F5, 31) (dual of [624, 526, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
  3. linear OA(5119, 624, F5, 38) (dual of [624, 505, 39]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−6,−5,…,31}, and designed minimum distance d ≥ |I|+1 = 39 [i]
  4. linear OA(594, 624, F5, 30) (dual of [624, 530, 31]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  5. linear OA(510, 28, F5, 6) (dual of [28, 18, 7]-code), using
    • construction X applied to Ce(5) ⊂ Ce(3) [i] based on
      1. linear OA(59, 25, F5, 6) (dual of [25, 16, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
      2. linear OA(57, 25, F5, 4) (dual of [25, 18, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
      3. linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
  6. linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-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

None.