Information on Result #1423160
Linear OOA(4138, 16431, F4, 2, 24) (dual of [(16431, 2), 32724, 25]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4138, 16431, F4, 24) (dual of [16431, 16293, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4137, 16429, F4, 24) (dual of [16429, 16292, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(410, 45, F4, 5) (dual of [45, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(4137, 16430, F4, 23) (dual of [16430, 16293, 24]-code), using Gilbert–Varšamov bound and bm = 4137 > Vbs−1(k−1) = 15255 657857 280173 740738 349388 552632 026673 955706 059433 198633 918126 604824 132532 693176 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(4137, 16429, F4, 24) (dual of [16429, 16292, 25]-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(4138, 8215, F4, 3, 24) (dual of [(8215, 3), 24507, 25]-NRT-code) | [i] | OOA Folding | |