Information on Result #612316

Linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46

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(3210, 2186, F3, 45) (dual of [2186, 1976, 46]-code) [i]Truncation
2Linear OA(3234, 2211, F3, 46) (dual of [2211, 1977, 47]-code) [i](u, u+v)-Construction
3Linear OOA(3211, 1593, F3, 2, 46) (dual of [(1593, 2), 2975, 47]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(3211, 1593, F3, 3, 46) (dual of [(1593, 3), 4568, 47]-NRT-code) [i]
5Linear OOA(3211, 1593, F3, 4, 46) (dual of [(1593, 4), 6161, 47]-NRT-code) [i]
6Linear OOA(3211, 1593, F3, 5, 46) (dual of [(1593, 5), 7754, 47]-NRT-code) [i]
7Digital (165, 211, 1593)-net over F3 [i]
8Linear OA(3223, 2238, F3, 46) (dual of [2238, 2015, 47]-code) [i]VarÅ¡amov–Edel Lengthening
9Linear OA(3224, 2254, F3, 46) (dual of [2254, 2030, 47]-code) [i]
10Linear OA(3225, 2274, F3, 46) (dual of [2274, 2049, 47]-code) [i]
11Linear OA(3226, 2299, F3, 46) (dual of [2299, 2073, 47]-code) [i]
12Linear OA(3227, 2329, F3, 46) (dual of [2329, 2102, 47]-code) [i]
13Linear OA(3228, 2366, F3, 46) (dual of [2366, 2138, 47]-code) [i]
14Linear OA(3229, 2409, F3, 46) (dual of [2409, 2180, 47]-code) [i]
15Linear OA(3230, 2457, F3, 46) (dual of [2457, 2227, 47]-code) [i]
16Linear OA(3231, 2510, F3, 46) (dual of [2510, 2279, 47]-code) [i]
17Linear OA(3232, 2567, F3, 46) (dual of [2567, 2335, 47]-code) [i]
18Linear OA(3233, 2628, F3, 46) (dual of [2628, 2395, 47]-code) [i]
19Linear OA(3234, 2691, F3, 46) (dual of [2691, 2457, 47]-code) [i]
20Linear OA(3235, 2757, F3, 46) (dual of [2757, 2522, 47]-code) [i]
21Linear OA(3218, 2194, F3, 47) (dual of [2194, 1976, 48]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
22Linear OA(3212, 2195, F3, 46) (dual of [2195, 1983, 47]-code) [i]✔
23Linear OA(3226, 2202, F3, 48) (dual of [2202, 1976, 49]-code) [i]✔
24Linear OA(3228, 2200, F3, 49) (dual of [2200, 1972, 50]-code) [i]✔
25Linear OA(3229, 2205, F3, 49) (dual of [2205, 1976, 50]-code) [i]✔
26Linear OA(3214, 2200, F3, 46) (dual of [2200, 1986, 47]-code) [i]✔
27Linear OA(3215, 2205, F3, 46) (dual of [2205, 1990, 47]-code) [i]✔
28Linear OA(3237, 2207, F3, 50) (dual of [2207, 1970, 51]-code) [i]✔
29Linear OA(3238, 2214, F3, 50) (dual of [2214, 1976, 51]-code) [i]✔
30Linear OA(3218, 2214, F3, 46) (dual of [2214, 1996, 47]-code) [i]✔
31Linear OA(3219, 2216, F3, 46) (dual of [2216, 1997, 47]-code) [i]✔
32Linear OA(3217, 2214, F3, 45) (dual of [2214, 1997, 46]-code) [i]✔
33Linear OA(3249, 2223, F3, 52) (dual of [2223, 1974, 53]-code) [i]✔
34Linear OA(3250, 2226, F3, 52) (dual of [2226, 1976, 53]-code) [i]✔
35Linear OA(3247, 2223, F3, 51) (dual of [2223, 1976, 52]-code) [i]✔
36Linear OA(3221, 2223, F3, 46) (dual of [2223, 2002, 47]-code) [i]✔
37Linear OA(3222, 2226, F3, 46) (dual of [2226, 2004, 47]-code) [i]✔
38Linear OA(3219, 2223, F3, 45) (dual of [2223, 2004, 46]-code) [i]✔
39Linear OA(3228, 2239, F3, 46) (dual of [2239, 2011, 47]-code) [i]✔
40Linear OA(3232, 2250, F3, 46) (dual of [2250, 2018, 47]-code) [i]✔
41Linear OA(3236, 2261, F3, 46) (dual of [2261, 2025, 47]-code) [i]✔
42Linear OA(3249, 2225, F3, 52) (dual of [2225, 1976, 53]-code) [i]✔
43Linear OA(3221, 2225, F3, 46) (dual of [2225, 2004, 47]-code) [i]✔
44Linear OA(3226, 2231, F3, 46) (dual of [2231, 2005, 47]-code) [i]✔
45Linear OA(3227, 2238, F3, 46) (dual of [2238, 2011, 47]-code) [i]✔
46Linear OA(3225, 2236, F3, 45) (dual of [2236, 2011, 46]-code) [i]✔
47Linear OA(3248, 2218, F3, 52) (dual of [2218, 1970, 53]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
48Linear OA(3246, 2216, F3, 51) (dual of [2216, 1970, 52]-code) [i]✔
49Linear OA(3241, 2219, F3, 50) (dual of [2219, 1978, 51]-code) [i]✔
50Linear OA(3240, 2217, F3, 50) (dual of [2217, 1977, 51]-code) [i]✔
51Linear OA(3227, 2197, F3, 49) (dual of [2197, 1970, 50]-code) [i]✔
52Linear OA(3230, 2209, F3, 48) (dual of [2209, 1979, 49]-code) [i]✔
53Linear OA(3229, 2207, F3, 48) (dual of [2207, 1978, 49]-code) [i]✔
54Linear OA(3228, 2205, F3, 48) (dual of [2205, 1977, 49]-code) [i]✔
55Linear OA(3220, 2197, F3, 47) (dual of [2197, 1977, 48]-code) [i]✔
56Linear OA(3213, 2197, F3, 46) (dual of [2197, 1984, 47]-code) [i]✔
57Linear OA(3216, 2209, F3, 45) (dual of [2209, 1993, 46]-code) [i]✔
58Linear OA(3215, 2207, F3, 45) (dual of [2207, 1992, 46]-code) [i]✔
59Linear OA(3217, 2208, F3, 46) (dual of [2208, 1991, 47]-code) [i]✔
60Linear OA(3220, 2218, F3, 46) (dual of [2218, 1998, 47]-code) [i]✔
61Linear OA(3218, 2216, F3, 45) (dual of [2216, 1998, 46]-code) [i]✔
62Linear OOA(3211, 1093, F3, 2, 46) (dual of [(1093, 2), 1975, 47]-NRT-code) [i]OOA Folding
63Linear OOA(3211, 729, F3, 3, 46) (dual of [(729, 3), 1976, 47]-NRT-code) [i]
64Linear OOA(3211, 546, F3, 4, 46) (dual of [(546, 4), 1973, 47]-NRT-code) [i]
65Linear OOA(3211, 437, F3, 5, 46) (dual of [(437, 5), 1974, 47]-NRT-code) [i]