Information on Result #678741
Linear OA(4112, 65575, F4, 18) (dual of [65575, 65463, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4113, 65576, F4, 18) (dual of [65576, 65463, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4114, 65577, F4, 18) (dual of [65577, 65463, 19]-code) | [i] | ||
| 3 | Linear OA(4115, 65578, F4, 18) (dual of [65578, 65463, 19]-code) | [i] | ||
| 4 | Linear OA(4116, 65579, F4, 18) (dual of [65579, 65463, 19]-code) | [i] | ||
| 5 | Linear OA(4117, 65580, F4, 18) (dual of [65580, 65463, 19]-code) | [i] | ||
| 6 | Linear OOA(4112, 34045, F4, 2, 18) (dual of [(34045, 2), 67978, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(4112, 34045, F4, 3, 18) (dual of [(34045, 3), 102023, 19]-NRT-code) | [i] | ||
| 8 | Digital (94, 112, 34045)-net over F4 | [i] | ||
| 9 | Linear OA(4114, 65578, F4, 18) (dual of [65578, 65464, 19]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4115, 65580, F4, 18) (dual of [65580, 65465, 19]-code) | [i] | ||
| 11 | Linear OA(4116, 65582, F4, 18) (dual of [65582, 65466, 19]-code) | [i] | ||
| 12 | Linear OA(4117, 65584, F4, 18) (dual of [65584, 65467, 19]-code) | [i] | ||
| 13 | Linear OOA(4112, 32787, F4, 2, 18) (dual of [(32787, 2), 65462, 19]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(4112, 21858, F4, 3, 18) (dual of [(21858, 3), 65462, 19]-NRT-code) | [i] | ||
| 15 | Linear OOA(4112, 7286, F4, 18, 18) (dual of [(7286, 18), 131036, 19]-NRT-code) | [i] | OA Folding and Stacking | |