Information on Result #709295

Linear OA(4223, 1066, F4, 57) (dual of [1066, 843, 58]-code), using construction XX applied to C1 = C([1019,48]), C2 = C([1,52]), C3 = C1 + C2 = C([1,48]), and C∩ = C1 ∩ C2 = C([1019,52]) based on
  1. linear OA(4196, 1023, F4, 53) (dual of [1023, 827, 54]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,48}, and designed minimum distance d ≥ |I|+1 = 54 [i]
  2. 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]
  3. linear OA(4211, 1023, F4, 57) (dual of [1023, 812, 58]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,52}, and designed minimum distance d ≥ |I|+1 = 58 [i]
  4. linear OA(4180, 1023, F4, 48) (dual of [1023, 843, 49]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
  5. linear OA(47, 23, F4, 4) (dual of [23, 16, 5]-code), using
  6. linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), 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(4224, 1067, F4, 57) (dual of [1067, 843, 58]-code) [i]Code Embedding in Larger Space
2Linear OA(4225, 1068, F4, 57) (dual of [1068, 843, 58]-code) [i]
3Linear OOA(4223, 533, F4, 2, 57) (dual of [(533, 2), 843, 58]-NRT-code) [i]OOA Folding
4Linear OOA(4223, 355, F4, 3, 57) (dual of [(355, 3), 842, 58]-NRT-code) [i]