Information on Result #682050

Linear OA(417, 71, F4, 7) (dual of [71, 54, 8]-code), using construction X applied to Ce(6) ⊂ Ce(4) based on
  1. linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
  2. linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
  3. linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-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.

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
1Linear OOA(417, 71, F4, 2, 7) (dual of [(71, 2), 125, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(417, 71, F4, 3, 7) (dual of [(71, 3), 196, 8]-NRT-code) [i]
3Digital (10, 17, 71)-net over F4 [i]
4Linear OA(4252, 262216, F4, 35) (dual of [262216, 261964, 36]-code) [i]Construction X with Cyclic Codes
5Linear OA(4234, 262216, F4, 33) (dual of [262216, 261982, 34]-code) [i]
6Linear OA(4198, 262216, F4, 27) (dual of [262216, 262018, 28]-code) [i]
7Linear OA(4180, 262216, F4, 25) (dual of [262216, 262036, 26]-code) [i]
8Linear OA(4243, 262215, F4, 34) (dual of [262215, 261972, 35]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
9Linear OA(4225, 262215, F4, 31) (dual of [262215, 261990, 32]-code) [i]
10Linear OA(4216, 262215, F4, 30) (dual of [262215, 261999, 31]-code) [i]
11Linear OA(4207, 262215, F4, 29) (dual of [262215, 262008, 30]-code) [i]
12Linear OA(4189, 262215, F4, 26) (dual of [262215, 262026, 27]-code) [i]