Information on Result #682980
Linear OA(542, 3131, F5, 11) (dual of [3131, 3089, 12]-code), using construction X applied to Ce(10) ⊂ Ce(8) based on
- linear OA(541, 3125, F5, 11) (dual of [3125, 3084, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(536, 3125, F5, 9) (dual of [3125, 3089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(51, 6, F5, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(541, 3130, F5, 10) (dual of [3130, 3089, 11]-code) | [i] | Truncation | |
| 2 | Linear OOA(542, 1579, F5, 2, 11) (dual of [(1579, 2), 3116, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(542, 1579, F5, 3, 11) (dual of [(1579, 3), 4695, 12]-NRT-code) | [i] | ||
| 4 | Digital (31, 42, 1579)-net over F5 | [i] | ||
| 5 | Linear OA(546, 3163, F5, 11) (dual of [3163, 3117, 12]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(547, 3204, F5, 11) (dual of [3204, 3157, 12]-code) | [i] | ||
| 7 | Linear OOA(542, 1565, F5, 2, 11) (dual of [(1565, 2), 3088, 12]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(542, 1043, F5, 3, 11) (dual of [(1043, 3), 3087, 12]-NRT-code) | [i] | ||
| 9 | Linear OOA(542, 626, F5, 11, 11) (dual of [(626, 11), 6844, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |