Information on Result #701588

Linear OA(875, 82, F8, 60) (dual of [82, 7, 61]-code), using construction X applied to C([0,42]) ⊂ C({1,2,3,4,5,6,7,9,11,12,13,14,17,18,25,26,27,33,34,35,36,42}) based on
  1. linear OA(870, 73, F8, 63) (dual of [73, 3, 64]-code), using the expurgated narrow-sense BCH-code C(I) with length 73 | 83−1, defining interval I = [0,42], and minimum distance d ≥ |{−20,−19,…,42}|+1 = 64 (BCH-bound) [i]
  2. linear OA(866, 73, F8, 54) (dual of [73, 7, 55]-code), using the cyclic code C(A) with length 73 | 83−1, defining set A = {1,2,3,4,5,6,7,9,11,12,13,14,17,18,25,26,27,33,34,35,36,42}, and minimum distance d ≥ |{−9,12,33,…,9}|+1 = 55 (BCH-bound) [i]
  3. linear OA(85, 9, F8, 5) (dual of [9, 4, 6]-code or 9-arc in PG(4,8)), 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(875, 82, F8, 59) (dual of [82, 7, 60]-code) [i]Strength Reduction
2Linear OA(875, 82, F8, 58) (dual of [82, 7, 59]-code) [i]
3Linear OA(874, 81, F8, 59) (dual of [81, 7, 60]-code) [i]Truncation
4Linear OA(873, 80, F8, 58) (dual of [80, 7, 59]-code) [i]
5Linear OA(872, 79, F8, 57) (dual of [79, 7, 58]-code) [i]
6Linear OA(897, 104, F8, 73) (dual of [104, 7, 74]-code) [i]Juxtaposition
7Linear OA(898, 105, F8, 74) (dual of [105, 7, 75]-code) [i]
8Linear OA(899, 106, F8, 75) (dual of [106, 7, 76]-code) [i]
9Linear OA(8147, 154, F8, 114) (dual of [154, 7, 115]-code) [i]
10Linear OA(8148, 155, F8, 115) (dual of [155, 7, 116]-code) [i]
11Linear OOA(875, 41, F8, 2, 60) (dual of [(41, 2), 7, 61]-NRT-code) [i]OOA Folding