Information on Result #1549383
Linear OOA(5115, 976579, F5, 3, 16) (dual of [(976579, 3), 2929622, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(5115, 976579, F5, 2, 16) (dual of [(976579, 2), 1953043, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5115, 1953158, F5, 16) (dual of [1953158, 1953043, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5114, 1953157, F5, 16) (dual of [1953157, 1953043, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(582, 1953125, F5, 12) (dual of [1953125, 1953043, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(55, 32, F5, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(5114, 1953157, F5, 16) (dual of [1953157, 1953043, 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(5115, 325526, F5, 21, 16) (dual of [(325526, 21), 6835931, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |