Information on Result #613914

Linear OA(5111, 3125, F5, 28) (dual of [3125, 3014, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28

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(5125, 3140, F5, 28) (dual of [3140, 3015, 29]-code) [i](u, u+v)-Construction
2Linear OA(5127, 3143, F5, 28) (dual of [3143, 3016, 29]-code) [i]
3Linear OA(5128, 3146, F5, 28) (dual of [3146, 3018, 29]-code) [i]
4Linear OA(5130, 3150, F5, 28) (dual of [3150, 3020, 29]-code) [i]
5Linear OA(5131, 3152, F5, 28) (dual of [3152, 3021, 29]-code) [i]
6Linear OOA(5111, 2372, F5, 2, 28) (dual of [(2372, 2), 4633, 29]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
7Linear OOA(5111, 2372, F5, 3, 28) (dual of [(2372, 3), 7005, 29]-NRT-code) [i]
8Digital (83, 111, 2372)-net over F5 [i]
9Linear OA(5130, 3145, F5, 28) (dual of [3145, 3015, 29]-code) [i](u, u−v, u+v+w)-Construction
10Linear OA(5116, 3130, F5, 29) (dual of [3130, 3014, 30]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
11Linear OA(5111, 3130, F5, 28) (dual of [3130, 3019, 29]-code) [i]✔
12Linear OA(5122, 3136, F5, 30) (dual of [3136, 3014, 31]-code) [i]✔
13Linear OA(5124, 3138, F5, 31) (dual of [3138, 3014, 32]-code) [i]✔
14Linear OA(5112, 3136, F5, 28) (dual of [3136, 3024, 29]-code) [i]✔
15Linear OA(5130, 3144, F5, 32) (dual of [3144, 3014, 33]-code) [i]✔
16Linear OA(5115, 3144, F5, 28) (dual of [3144, 3029, 29]-code) [i]✔
17Linear OA(5138, 3151, F5, 33) (dual of [3151, 3013, 34]-code) [i]✔
18Linear OA(5139, 3153, F5, 33) (dual of [3153, 3014, 34]-code) [i]✔
19Linear OA(5118, 3151, F5, 28) (dual of [3151, 3033, 29]-code) [i]✔
20Linear OA(5119, 3153, F5, 28) (dual of [3153, 3034, 29]-code) [i]✔
21Linear OA(5146, 3160, F5, 34) (dual of [3160, 3014, 35]-code) [i]✔
22Linear OA(5121, 3160, F5, 28) (dual of [3160, 3039, 29]-code) [i]✔
23Linear OA(5123, 3167, F5, 28) (dual of [3167, 3044, 29]-code) [i]✔
24Linear OA(5127, 3176, F5, 28) (dual of [3176, 3049, 29]-code) [i]✔
25Linear OA(5131, 3183, F5, 28) (dual of [3183, 3052, 29]-code) [i]✔
26Linear OA(5137, 3151, F5, 33) (dual of [3151, 3014, 34]-code) [i]✔
27Linear OA(5117, 3151, F5, 28) (dual of [3151, 3034, 29]-code) [i]✔
28Linear OA(5143, 3153, F5, 34) (dual of [3153, 3010, 35]-code) [i]✔
29Linear OA(5144, 3158, F5, 34) (dual of [3158, 3014, 35]-code) [i]✔
30Linear OA(5118, 3153, F5, 28) (dual of [3153, 3035, 29]-code) [i]✔
31Linear OA(5119, 3158, F5, 28) (dual of [3158, 3039, 29]-code) [i]✔
32Linear OA(5122, 3166, F5, 28) (dual of [3166, 3044, 29]-code) [i]✔
33Linear OA(5130, 3181, F5, 28) (dual of [3181, 3051, 29]-code) [i]✔
34Linear OA(5145, 3155, F5, 34) (dual of [3155, 3010, 35]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
35Linear OA(5137, 3148, F5, 33) (dual of [3148, 3011, 34]-code) [i]✔
36Linear OA(5136, 3146, F5, 33) (dual of [3146, 3010, 34]-code) [i]✔
37Linear OA(5140, 3155, F5, 33) (dual of [3155, 3015, 34]-code) [i]✔
38Linear OA(5132, 3148, F5, 32) (dual of [3148, 3016, 33]-code) [i]✔
39Linear OA(5131, 3146, F5, 32) (dual of [3146, 3015, 33]-code) [i]✔
40Linear OA(5123, 3133, F5, 31) (dual of [3133, 3010, 32]-code) [i]✔
41Linear OA(5123, 3138, F5, 30) (dual of [3138, 3015, 31]-code) [i]✔
42Linear OA(5114, 3139, F5, 28) (dual of [3139, 3025, 29]-code) [i]✔
43Linear OA(5117, 3148, F5, 28) (dual of [3148, 3031, 29]-code) [i]✔
44Linear OA(5116, 3146, F5, 28) (dual of [3146, 3030, 29]-code) [i]✔
45Linear OA(5120, 3155, F5, 28) (dual of [3155, 3035, 29]-code) [i]✔