Information on Result #682019

Linear OA(469, 77, F4, 49) (dual of [77, 8, 50]-code), using construction X applied to C([0,25]) ⊂ C([0,21]) based on
  1. linear OA(463, 65, F4, 51) (dual of [65, 2, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,25], and minimum distance d ≥ |{−15,−4,7,…,15}|+1 = 52 (BCH-bound) [i]
  2. linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
  3. linear OA(46, 12, F4, 5) (dual of [12, 6, 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(469, 77, F4, 48) (dual of [77, 8, 49]-code) [i]Strength Reduction
2Linear OA(469, 77, F4, 47) (dual of [77, 8, 48]-code) [i]
3Linear OA(468, 76, F4, 48) (dual of [76, 8, 49]-code) [i]Truncation
4Linear OA(463, 71, F4, 43) (dual of [71, 8, 44]-code) [i]
5Linear OA(460, 68, F4, 40) (dual of [68, 8, 41]-code) [i]
6Linear OA(459, 67, F4, 39) (dual of [67, 8, 40]-code) [i]
7Linear OA(4144, 150, F4, 99) (dual of [150, 6, 100]-code) [i]Repeating Each Code Word
8Linear OA(4133, 141, F4, 92) (dual of [141, 8, 93]-code) [i]Juxtaposition
9Linear OA(4134, 142, F4, 93) (dual of [142, 8, 94]-code) [i]
10Linear OA(2213, 225, F2, 99) (dual of [225, 12, 100]-code) [i]Concatenation of Two Codes
11Linear OA(2212, 222, F2, 99) (dual of [222, 10, 100]-code) [i]
12Linear OA(2215, 231, F2, 99) (dual of [231, 16, 100]-code) [i]