Information on Result #683223
Linear OA(548, 3133, F5, 12) (dual of [3133, 3085, 13]-code), using construction XX applied to Ce(11) ⊂ Ce(10) ⊂ Ce(8) based on
- linear OA(546, 3125, F5, 12) (dual of [3125, 3079, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- 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(50, 6, F5, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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 OOA(548, 2177, F5, 2, 12) (dual of [(2177, 2), 4306, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(548, 2177, F5, 3, 12) (dual of [(2177, 3), 6483, 13]-NRT-code) | [i] | ||
| 3 | Digital (36, 48, 2177)-net over F5 | [i] | ||
| 4 | Linear OOA(548, 1044, F5, 3, 12) (dual of [(1044, 3), 3084, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(548, 522, F5, 12, 12) (dual of [(522, 12), 6216, 13]-NRT-code) | [i] | OA Folding and Stacking | |