Information on Result #709550

Linear OA(4253, 1081, F4, 63) (dual of [1081, 828, 64]-code), using construction XX applied to C1 = C([1018,52]), C2 = C([1,57]), C3 = C1 + C2 = C([1,52]), and C∩ = C1 ∩ C2 = C([1018,57]) based on
  1. linear OA(4216, 1023, F4, 58) (dual of [1023, 807, 59]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,52}, and designed minimum distance d ≥ |I|+1 = 59 [i]
  2. linear OA(4215, 1023, F4, 57) (dual of [1023, 808, 58]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,57], and designed minimum distance d ≥ |I|+1 = 58 [i]
  3. linear OA(4236, 1023, F4, 63) (dual of [1023, 787, 64]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,57}, and designed minimum distance d ≥ |I|+1 = 64 [i]
  4. linear OA(4195, 1023, F4, 52) (dual of [1023, 828, 53]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
  5. linear OA(410, 31, F4, 5) (dual of [31, 21, 6]-code), using
  6. linear OA(47, 27, F4, 4) (dual of [27, 20, 5]-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(4254, 1082, F4, 63) (dual of [1082, 828, 64]-code) [i]Code Embedding in Larger Space