Information on Result #709728

Linear OA(513, 124, F5, 6) (dual of [124, 111, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7

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

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(513, 67, F5, 2, 6) (dual of [(67, 2), 121, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(513, 67, F5, 3, 6) (dual of [(67, 3), 188, 7]-NRT-code) [i]
3Digital (7, 13, 67)-net over F5 [i]
4Linear OA(518, 133, F5, 7) (dual of [133, 115, 8]-code) [i]✔Construction XX with Cyclic Codes
5Linear OA(522, 137, F5, 8) (dual of [137, 115, 9]-code) [i]✔
6Linear OA(521, 135, F5, 8) (dual of [135, 114, 9]-code) [i]✔
7Linear OA(530, 144, F5, 10) (dual of [144, 114, 11]-code) [i]✔
8Linear OA(519, 130, F5, 8) (dual of [130, 111, 9]-code) [i]✔
9Linear OA(523, 134, F5, 9) (dual of [134, 111, 10]-code) [i]✔
10Linear OA(528, 139, F5, 10) (dual of [139, 111, 11]-code) [i]✔
11Linear OA(534, 145, F5, 12) (dual of [145, 111, 13]-code) [i]✔
12Linear OA(527, 138, F5, 10) (dual of [138, 111, 11]-code) [i]✔
13Linear OA(5149, 1953192, F5, 19) (dual of [1953192, 1953043, 20]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
14Linear OA(5140, 1953192, F5, 18) (dual of [1953192, 1953052, 19]-code) [i]
15Linear OOA(513, 62, F5, 2, 6) (dual of [(62, 2), 111, 7]-NRT-code) [i]OOA Folding
16Linear OOA(513, 41, F5, 3, 6) (dual of [(41, 3), 110, 7]-NRT-code) [i]