Information on Result #1301770
Linear OA(5118, 1953171, F5, 16) (dual of [1953171, 1953053, 17]-code), using construction X with Varšamov bound based on
- linear OA(5116, 1953168, F5, 16) (dual of [1953168, 1953052, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [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(573, 1953125, F5, 11) (dual of [1953125, 1953052, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(57, 43, F5, 4) (dual of [43, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(5116, 1953169, F5, 14) (dual of [1953169, 1953053, 15]-code), using Gilbert–Varšamov bound and bm = 5116 > Vbs−1(k−1) = 64 878044 968003 755515 428544 848657 862496 611044 410731 349777 461010 913781 995514 526145 [i]
- linear OA(51, 2, F5, 1) (dual of [2, 1, 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: 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(5118, 651057, F5, 3, 16) (dual of [(651057, 3), 1953053, 17]-NRT-code) | [i] | OOA Folding | |