Information on Result #1437441
Linear OOA(582, 15660, F5, 2, 16) (dual of [(15660, 2), 31238, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(582, 15660, F5, 16) (dual of [15660, 15578, 17]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(579, 15655, F5, 16) (dual of [15655, 15576, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(579, 15657, F5, 14) (dual of [15657, 15578, 15]-code), using Gilbert–Varšamov bound and bm = 579 > Vbs−1(k−1) = 36414 645419 717975 589858 772363 055759 268814 797924 073825 [i]
- linear OA(51, 3, F5, 1) (dual of [3, 2, 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
- linear OA(579, 15655, F5, 16) (dual of [15655, 15576, 17]-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(582, 7830, F5, 3, 16) (dual of [(7830, 3), 23408, 17]-NRT-code) | [i] | OOA Folding | |