Information on Result #737970

Linear OA(457, 84, F4, 28) (dual of [84, 27, 29]-code), using construction X applied to C({1,3,5,7,9,10,11,13,22}) ⊂ C({1,3,5,7,9,11,13}) based on
  1. linear OA(450, 65, F4, 30) (dual of [65, 15, 31]-code), using the cyclic code C(A) with length 65 | 46−1, defining set A = {1,3,5,7,9,10,11,13,22}, and minimum distance d ≥ |{−29,−27,−25,…,29}|+1 = 31 (BCH-bound) [i]
  2. linear OA(438, 65, F4, 22) (dual of [65, 27, 23]-code), using the cyclic code C(A) with length 65 | 46−1, defining set A = {1,3,5,7,9,11,13}, and minimum distance d ≥ |{−21,−19,−17,…,21}|+1 = 23 (BCH-bound) [i]
  3. linear OA(47, 19, F4, 5) (dual of [19, 12, 6]-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 OA(457, 84, F4, 27) (dual of [84, 27, 28]-code) [i]Strength Reduction
2Linear OA(4140, 166, F4, 57) (dual of [166, 26, 58]-code) [i]Repeating Each Code Word
3Linear OA(4139, 164, F4, 57) (dual of [164, 25, 58]-code) [i]
4Linear OA(4138, 162, F4, 57) (dual of [162, 24, 58]-code) [i]
5Linear OA(4137, 160, F4, 57) (dual of [160, 23, 58]-code) [i]
6Linear OA(4136, 158, F4, 57) (dual of [158, 22, 58]-code) [i]
7Linear OA(4135, 156, F4, 57) (dual of [156, 21, 58]-code) [i]
8Linear OA(4134, 154, F4, 57) (dual of [154, 20, 58]-code) [i]
9Linear OA(4133, 152, F4, 57) (dual of [152, 19, 58]-code) [i]
10Linear OA(4132, 150, F4, 57) (dual of [150, 18, 58]-code) [i]
11Linear OA(4131, 148, F4, 57) (dual of [148, 17, 58]-code) [i]
12Linear OA(458, 86, F4, 28) (dual of [86, 28, 29]-code) [i]Construction X with VarÅ¡amov Bound
13Linear OOA(457, 42, F4, 2, 28) (dual of [(42, 2), 27, 29]-NRT-code) [i]OOA Folding
14Linear OOA(457, 28, F4, 3, 28) (dual of [(28, 3), 27, 29]-NRT-code) [i]