Information on Result #1301901
Linear OA(5141, 1953158, F5, 19) (dual of [1953158, 1953017, 20]-code), using construction X with Varšamov bound based on
- linear OA(5139, 1953155, F5, 19) (dual of [1953155, 1953016, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(5136, 1953125, F5, 19) (dual of [1953125, 1952989, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(53, 30, F5, 2) (dual of [30, 27, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(5139, 1953156, F5, 17) (dual of [1953156, 1953017, 18]-code), using Gilbert–Varšamov bound and bm = 5139 > Vbs−1(k−1) = 9 206654 168500 647825 118715 836086 011569 979134 216405 880488 304020 835392 366949 187549 235988 932130 071165 [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(5141, 976579, F5, 2, 19) (dual of [(976579, 2), 1953017, 20]-NRT-code) | [i] | OOA Folding | |