Information on Result #547877

There is no linear OA(4141, 163, F4, 104) (dual of [163, 22, 105]-code), because construction Y1 would yield
  1. OA(4140, 151, S4, 104), but
    • 2 times truncation [i] would yield OA(4138, 149, S4, 102), but
      • the linear programming bound shows that M ≥ 11 769278 720446 703333 267659 747956 551886 187319 922656 933070 157940 129170 842786 675855 465333 653504 / 85 907459 > 4138 [i]
  2. OA(422, 163, S4, 12), but

Mode: Bound (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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1No linear OA(4142, 164, F4, 105) (dual of [164, 22, 106]-code) [i]Truncation
2No linear OA(4143, 165, F4, 106) (dual of [165, 22, 107]-code) [i]
3No linear OA(4144, 166, F4, 107) (dual of [166, 22, 108]-code) [i]
4No linear OA(4145, 167, F4, 108) (dual of [167, 22, 109]-code) [i]
5No linear OA(4146, 168, F4, 109) (dual of [168, 22, 110]-code) [i]
6No linear OA(4147, 169, F4, 110) (dual of [169, 22, 111]-code) [i]
7No linear OA(4148, 170, F4, 111) (dual of [170, 22, 112]-code) [i]
8No linear OOA(4141, 163, F4, 2, 104) (dual of [(163, 2), 185, 105]-NRT-code) [i]Depth Reduction
9No linear OOA(4141, 163, F4, 3, 104) (dual of [(163, 3), 348, 105]-NRT-code) [i]
10No linear OA(4142, 199, F4, 104) (dual of [199, 57, 105]-code) [i]Construction Y1 (Bound)