Information on Result #614414

Linear OA(725, 50, F7, 17) (dual of [50, 25, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 50 | 74−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound)

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(725, 50, F7, 16) (dual of [50, 25, 17]-code) [i]Strength Reduction
2Linear OA(726, 51, F7, 17) (dual of [51, 25, 18]-code) [i]Code Embedding in Larger Space
3Linear OA(722, 47, F7, 14) (dual of [47, 25, 15]-code) [i]Truncation
4Linear OA(721, 46, F7, 13) (dual of [46, 25, 14]-code) [i]
5Linear OA(732, 66, F7, 17) (dual of [66, 34, 18]-code) [i]VarÅ¡amov–Edel Lengthening
6Linear OA(733, 72, F7, 17) (dual of [72, 39, 18]-code) [i]
7Linear OA(732, 58, F7, 17) (dual of [58, 26, 18]-code) [i]✔Construction X with Cyclic Codes
8Linear OA(730, 55, F7, 19) (dual of [55, 25, 20]-code) [i]✔
9Linear OA(730, 58, F7, 17) (dual of [58, 28, 18]-code) [i]✔
10Linear OA(731, 60, F7, 17) (dual of [60, 29, 18]-code) [i]✔
11Linear OA(729, 58, F7, 16) (dual of [58, 29, 17]-code) [i]✔
12Linear OA(736, 58, F7, 21) (dual of [58, 22, 22]-code) [i]✔
13Linear OA(737, 62, F7, 21) (dual of [62, 25, 22]-code) [i]✔
14Linear OA(735, 58, F7, 20) (dual of [58, 23, 21]-code) [i]✔
15Linear OA(744, 69, F7, 23) (dual of [69, 25, 24]-code) [i]✔
16Linear OA(737, 64, F7, 19) (dual of [64, 27, 20]-code) [i]✔Construction XX with a Chain of Cyclic Codes
17Linear OA(736, 62, F7, 19) (dual of [62, 26, 20]-code) [i]✔
18Linear OA(733, 63, F7, 17) (dual of [63, 30, 18]-code) [i]✔
19Linear OOA(725, 25, F7, 2, 17) (dual of [(25, 2), 25, 18]-NRT-code) [i]OOA Folding