Information on Result #613758

Linear OA(571, 3125, F5, 18) (dual of [3125, 3054, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18

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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(580, 3135, F5, 18) (dual of [3135, 3055, 19]-code) [i](u, u+v)-Construction
2Linear OA(581, 3137, F5, 18) (dual of [3137, 3056, 19]-code) [i]
3Linear OA(582, 3139, F5, 18) (dual of [3139, 3057, 19]-code) [i]
4Linear OA(583, 3141, F5, 18) (dual of [3141, 3058, 19]-code) [i]
5Linear OOA(571, 1932, F5, 2, 18) (dual of [(1932, 2), 3793, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(571, 1932, F5, 3, 18) (dual of [(1932, 3), 5725, 19]-NRT-code) [i]
7Digital (53, 71, 1932)-net over F5 [i]
8Linear OA(576, 3130, F5, 19) (dual of [3130, 3054, 20]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
9Linear OA(571, 3130, F5, 18) (dual of [3130, 3059, 19]-code) [i]✔
10Linear OA(582, 3136, F5, 20) (dual of [3136, 3054, 21]-code) [i]✔
11Linear OA(584, 3138, F5, 21) (dual of [3138, 3054, 22]-code) [i]✔
12Linear OA(572, 3136, F5, 18) (dual of [3136, 3064, 19]-code) [i]✔
13Linear OA(590, 3144, F5, 22) (dual of [3144, 3054, 23]-code) [i]✔
14Linear OA(575, 3144, F5, 18) (dual of [3144, 3069, 19]-code) [i]✔
15Linear OA(598, 3151, F5, 23) (dual of [3151, 3053, 24]-code) [i]✔
16Linear OA(599, 3153, F5, 23) (dual of [3153, 3054, 24]-code) [i]✔
17Linear OA(578, 3151, F5, 18) (dual of [3151, 3073, 19]-code) [i]✔
18Linear OA(579, 3153, F5, 18) (dual of [3153, 3074, 19]-code) [i]✔
19Linear OA(5106, 3160, F5, 24) (dual of [3160, 3054, 25]-code) [i]✔
20Linear OA(581, 3160, F5, 18) (dual of [3160, 3079, 19]-code) [i]✔
21Linear OA(5115, 3169, F5, 26) (dual of [3169, 3054, 27]-code) [i]✔
22Linear OA(5113, 3167, F5, 25) (dual of [3167, 3054, 26]-code) [i]✔
23Linear OA(583, 3167, F5, 18) (dual of [3167, 3084, 19]-code) [i]✔
24Linear OA(5122, 3176, F5, 27) (dual of [3176, 3054, 28]-code) [i]✔
25Linear OA(5131, 3183, F5, 28) (dual of [3183, 3052, 29]-code) [i]✔
26Linear OA(597, 3151, F5, 23) (dual of [3151, 3054, 24]-code) [i]✔
27Linear OA(577, 3151, F5, 18) (dual of [3151, 3074, 19]-code) [i]✔
28Linear OA(5103, 3153, F5, 24) (dual of [3153, 3050, 25]-code) [i]✔
29Linear OA(5104, 3158, F5, 24) (dual of [3158, 3054, 25]-code) [i]✔
30Linear OA(578, 3153, F5, 18) (dual of [3153, 3075, 19]-code) [i]✔
31Linear OA(579, 3158, F5, 18) (dual of [3158, 3079, 19]-code) [i]✔
32Linear OA(5112, 3166, F5, 25) (dual of [3166, 3054, 26]-code) [i]✔
33Linear OA(582, 3166, F5, 18) (dual of [3166, 3084, 19]-code) [i]✔
34Linear OA(5130, 3181, F5, 28) (dual of [3181, 3051, 29]-code) [i]✔
35Linear OA(5105, 3155, F5, 24) (dual of [3155, 3050, 25]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
36Linear OA(597, 3148, F5, 23) (dual of [3148, 3051, 24]-code) [i]✔
37Linear OA(596, 3146, F5, 23) (dual of [3146, 3050, 24]-code) [i]✔
38Linear OA(5100, 3155, F5, 23) (dual of [3155, 3055, 24]-code) [i]✔
39Linear OA(592, 3148, F5, 22) (dual of [3148, 3056, 23]-code) [i]✔
40Linear OA(591, 3146, F5, 22) (dual of [3146, 3055, 23]-code) [i]✔
41Linear OA(583, 3133, F5, 21) (dual of [3133, 3050, 22]-code) [i]✔
42Linear OA(583, 3138, F5, 20) (dual of [3138, 3055, 21]-code) [i]✔
43Linear OA(574, 3139, F5, 18) (dual of [3139, 3065, 19]-code) [i]✔
44Linear OA(577, 3148, F5, 18) (dual of [3148, 3071, 19]-code) [i]✔
45Linear OA(576, 3146, F5, 18) (dual of [3146, 3070, 19]-code) [i]✔
46Linear OA(580, 3155, F5, 18) (dual of [3155, 3075, 19]-code) [i]✔
47Linear OOA(571, 347, F5, 18, 18) (dual of [(347, 18), 6175, 19]-NRT-code) [i]OA Folding and Stacking