Information on Result #682145
Linear OA(538, 1953136, F5, 6) (dual of [1953136, 1953098, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(3) based on
- linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(528, 1953125, F5, 4) (dual of [1953125, 1953097, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(510, 11, F5, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,5)), using
- dual of repetition code with length 11 [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 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(539, 1953137, F5, 6) (dual of [1953137, 1953098, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(537, 1953135, F5, 5) (dual of [1953135, 1953098, 6]-code) | [i] | Truncation | |
| 3 | Linear OA(539, 1953138, F5, 6) (dual of [1953138, 1953099, 7]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(538, 976568, F5, 2, 6) (dual of [(976568, 2), 1953098, 7]-NRT-code) | [i] | OOA Folding | |