Information on Result #682131
Linear OA(5110, 1953135, F5, 16) (dual of [1953135, 1953025, 17]-code), using construction X applied to Ce(15) ⊂ Ce(13) 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(5100, 1953125, F5, 14) (dual of [1953125, 1953025, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(51, 10, F5, 1) (dual of [10, 9, 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(5111, 1953136, F5, 16) (dual of [1953136, 1953025, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5109, 1953134, F5, 15) (dual of [1953134, 1953025, 16]-code) | [i] | Truncation | |
| 3 | Linear OOA(5110, 976567, F5, 2, 16) (dual of [(976567, 2), 1953024, 17]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(5110, 651045, F5, 3, 16) (dual of [(651045, 3), 1953025, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(5110, 244141, F5, 16, 16) (dual of [(244141, 16), 3906146, 17]-NRT-code) | [i] | OA Folding and Stacking | |