Information on Result #709107

Linear OA(4211, 1073, F4, 53) (dual of [1073, 862, 54]-code), using construction XX applied to C1 = C([301,349]), C2 = C([297,343]), C3 = C1 + C2 = C([301,343]), and C∩ = C1 ∩ C2 = C([297,349]) based on
  1. linear OA(4181, 1023, F4, 49) (dual of [1023, 842, 50]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {301,302,…,349}, and designed minimum distance d ≥ |I|+1 = 50 [i]
  2. linear OA(4176, 1023, F4, 47) (dual of [1023, 847, 48]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {297,298,…,343}, and designed minimum distance d ≥ |I|+1 = 48 [i]
  3. 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 = {297,298,…,349}, and designed minimum distance d ≥ |I|+1 = 54 [i]
  4. linear OA(4161, 1023, F4, 43) (dual of [1023, 862, 44]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {301,302,…,343}, and designed minimum distance d ≥ |I|+1 = 44 [i]
  5. linear OA(410, 30, F4, 5) (dual of [30, 20, 6]-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(4212, 1074, F4, 53) (dual of [1074, 862, 54]-code) [i]Code Embedding in Larger Space
2Linear OOA(4211, 536, F4, 2, 53) (dual of [(536, 2), 861, 54]-NRT-code) [i]OOA Folding
3Linear OOA(4211, 357, F4, 3, 53) (dual of [(357, 3), 860, 54]-NRT-code) [i]