Information on Result #1436472
Linear OOA(539, 1953138, F5, 2, 6) (dual of [(1953138, 2), 3906237, 7]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(539, 1953138, F5, 6) (dual of [1953138, 1953099, 7]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(538, 1953136, F5, 6) (dual of [1953136, 1953098, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] 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
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(538, 1953137, F5, 5) (dual of [1953137, 1953099, 6]-code), using Gilbert–Varšamov bound and bm = 538 > Vbs−1(k−1) = 155 223528 567291 336789 158465 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 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(538, 1953136, F5, 6) (dual of [1953136, 1953098, 7]-code), using
Mode: 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(539, 976569, F5, 3, 6) (dual of [(976569, 3), 2929668, 7]-NRT-code) | [i] | OOA Folding | |