Information on Result #1547821
Linear OOA(571, 15648, F5, 3, 14) (dual of [(15648, 3), 46873, 15]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(571, 15648, F5, 14) (dual of [15648, 15577, 15]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(570, 15646, F5, 14) (dual of [15646, 15576, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(53, 21, F5, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(570, 15647, F5, 13) (dual of [15647, 15577, 14]-code), using Gilbert–Varšamov bound and bm = 570 > Vbs−1(k−1) = 7 507126 497762 266353 326085 184394 983313 062616 834985 [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(570, 15646, F5, 14) (dual of [15646, 15576, 15]-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(571, 5215, F5, 21, 14) (dual of [(5215, 21), 109444, 15]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |