Information on Result #612366

Linear OA(3239, 2187, F3, 52) (dual of [2187, 1948, 53]-code), using an extension Ce(51) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52

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(3238, 2186, F3, 51) (dual of [2186, 1948, 52]-code) [i]Truncation
2Linear OOA(3239, 1773, F3, 2, 52) (dual of [(1773, 2), 3307, 53]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(3239, 1773, F3, 3, 52) (dual of [(1773, 3), 5080, 53]-NRT-code) [i]
4Linear OOA(3239, 1773, F3, 4, 52) (dual of [(1773, 4), 6853, 53]-NRT-code) [i]
5Linear OOA(3239, 1773, F3, 5, 52) (dual of [(1773, 5), 8626, 53]-NRT-code) [i]
6Digital (187, 239, 1773)-net over F3 [i]
7Linear OA(3248, 2224, F3, 52) (dual of [2224, 1976, 53]-code) [i]VarÅ¡amov–Edel Lengthening
8Linear OA(3249, 2238, F3, 52) (dual of [2238, 1989, 53]-code) [i]
9Linear OA(3250, 2257, F3, 52) (dual of [2257, 2007, 53]-code) [i]
10Linear OA(3246, 2194, F3, 53) (dual of [2194, 1948, 54]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
11Linear OA(3240, 2195, F3, 52) (dual of [2195, 1955, 53]-code) [i]✔
12Linear OA(3242, 2200, F3, 52) (dual of [2200, 1958, 53]-code) [i]✔
13Linear OA(3243, 2205, F3, 52) (dual of [2205, 1962, 53]-code) [i]✔
14Linear OA(3246, 2214, F3, 52) (dual of [2214, 1968, 53]-code) [i]✔
15Linear OA(3247, 2216, F3, 52) (dual of [2216, 1969, 53]-code) [i]✔
16Linear OA(3245, 2214, F3, 51) (dual of [2214, 1969, 52]-code) [i]✔
17Linear OA(3249, 2223, F3, 52) (dual of [2223, 1974, 53]-code) [i]✔
18Linear OA(3250, 2226, F3, 52) (dual of [2226, 1976, 53]-code) [i]✔
19Linear OA(3247, 2223, F3, 51) (dual of [2223, 1976, 52]-code) [i]✔
20Linear OA(3249, 2225, F3, 52) (dual of [2225, 1976, 53]-code) [i]✔
21Linear OA(3248, 2197, F3, 53) (dual of [2197, 1949, 54]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
22Linear OA(3241, 2197, F3, 52) (dual of [2197, 1956, 53]-code) [i]✔
23Linear OA(3244, 2209, F3, 51) (dual of [2209, 1965, 52]-code) [i]✔
24Linear OA(3243, 2207, F3, 51) (dual of [2207, 1964, 52]-code) [i]✔
25Linear OA(3245, 2208, F3, 52) (dual of [2208, 1963, 53]-code) [i]✔
26Linear OA(3248, 2218, F3, 52) (dual of [2218, 1970, 53]-code) [i]✔
27Linear OA(3246, 2216, F3, 51) (dual of [2216, 1970, 52]-code) [i]✔
28Linear OOA(3239, 1093, F3, 2, 52) (dual of [(1093, 2), 1947, 53]-NRT-code) [i]OOA Folding
29Linear OOA(3239, 729, F3, 3, 52) (dual of [(729, 3), 1948, 53]-NRT-code) [i]
30Linear OOA(3239, 546, F3, 4, 52) (dual of [(546, 4), 1945, 53]-NRT-code) [i]
31Linear OOA(3239, 437, F3, 5, 52) (dual of [(437, 5), 1946, 53]-NRT-code) [i]