Information on Result #612558

Linear OA(3217, 243, F3, 125) (dual of [243, 26, 126]-code), using an extension Ce(124) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,124], and designed minimum distance d ≥ |I|+1 = 125

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

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(3217, 243, F3, 124) (dual of [243, 26, 125]-code) [i]Strength Reduction
2Linear OA(3218, 244, F3, 125) (dual of [244, 26, 126]-code) [i]Code Embedding in Larger Space
3Linear OA(3215, 241, F3, 123) (dual of [241, 26, 124]-code) [i]Truncation
4Linear OA(3243, 269, F3, 126) (dual of [269, 26, 127]-code) [i]Juxtaposition
5Linear OA(3244, 270, F3, 127) (dual of [270, 26, 128]-code) [i]
6Linear OA(3247, 273, F3, 128) (dual of [273, 26, 129]-code) [i]
7Linear OA(3249, 275, F3, 129) (dual of [275, 26, 130]-code) [i]
8Linear OA(392, 117, F3, 41) (dual of [117, 25, 42]-code) [i]Residual Code
9Linear OA(3223, 249, F3, 127) (dual of [249, 26, 128]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
10Linear OA(3227, 249, F3, 131) (dual of [249, 22, 132]-code) [i]✔
11Linear OA(3228, 254, F3, 131) (dual of [254, 26, 132]-code) [i]✔
12Linear OA(3224, 247, F3, 128) (dual of [247, 23, 129]-code) [i]✔
13Linear OA(3218, 249, F3, 124) (dual of [249, 31, 125]-code) [i]✔
14Linear OA(3219, 247, F3, 125) (dual of [247, 28, 126]-code) [i]✔
15Linear OA(3220, 251, F3, 125) (dual of [251, 31, 126]-code) [i]✔
16Linear OA(3239, 265, F3, 134) (dual of [265, 26, 135]-code) [i]✔
17Linear OA(3218, 250, F3, 123) (dual of [250, 32, 124]-code) [i]✔
18Linear OA(3221, 253, F3, 125) (dual of [253, 32, 126]-code) [i]✔
19Linear OA(3250, 276, F3, 135) (dual of [276, 26, 136]-code) [i]✔
20Linear OA(3250, 272, F3, 136) (dual of [272, 22, 137]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
21Linear OA(3250, 276, F3, 136) (dual of [276, 26, 137]-code) [i]✔
22Linear OA(3248, 274, F3, 135) (dual of [274, 26, 136]-code) [i]✔
23Linear OA(3250, 275, F3, 137) (dual of [275, 25, 138]-code) [i]✔
24Linear OA(3247, 272, F3, 135) (dual of [272, 25, 136]-code) [i]✔
25Linear OA(3249, 273, F3, 137) (dual of [273, 24, 138]-code) [i]✔
26Linear OA(3246, 270, F3, 135) (dual of [270, 24, 136]-code) [i]✔
27Linear OA(3250, 273, F3, 138) (dual of [273, 23, 139]-code) [i]✔
28Linear OA(3248, 271, F3, 137) (dual of [271, 23, 138]-code) [i]✔
29Linear OA(3245, 268, F3, 135) (dual of [268, 23, 136]-code) [i]✔
30Linear OA(3250, 272, F3, 140) (dual of [272, 22, 141]-code) [i]✔
31Linear OA(3246, 268, F3, 137) (dual of [268, 22, 138]-code) [i]✔
32Linear OA(3243, 265, F3, 135) (dual of [265, 22, 136]-code) [i]✔
33Linear OA(3237, 261, F3, 133) (dual of [261, 24, 134]-code) [i]✔
34Linear OA(3238, 261, F3, 134) (dual of [261, 23, 135]-code) [i]✔
35Linear OA(3236, 259, F3, 133) (dual of [259, 23, 134]-code) [i]✔
36Linear OA(3236, 258, F3, 134) (dual of [258, 22, 135]-code) [i]✔
37Linear OA(3234, 256, F3, 133) (dual of [256, 22, 134]-code) [i]✔
38Linear OA(3244, 273, F3, 132) (dual of [273, 29, 133]-code) [i]✔
39Linear OA(3243, 271, F3, 134) (dual of [271, 28, 135]-code) [i]✔
40Linear OA(3242, 269, F3, 134) (dual of [269, 27, 135]-code) [i]✔
41Linear OA(3233, 261, F3, 131) (dual of [261, 28, 132]-code) [i]✔
42Linear OA(3227, 255, F3, 127) (dual of [255, 28, 128]-code) [i]✔
43Linear OA(3231, 258, F3, 131) (dual of [258, 27, 132]-code) [i]✔
44Linear OA(3226, 253, F3, 127) (dual of [253, 27, 128]-code) [i]✔
45Linear OA(3219, 251, F3, 124) (dual of [251, 32, 125]-code) [i]✔
46Linear OOA(3217, 81, F3, 3, 125) (dual of [(81, 3), 26, 126]-NRT-code) [i]OOA Folding