Information on Result #1535827
Linear OOA(4110, 16431, F4, 3, 19) (dual of [(16431, 3), 49183, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4110, 16431, F4, 19) (dual of [16431, 16321, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4109, 16429, F4, 19) (dual of [16429, 16320, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(464, 16384, F4, 13) (dual of [16384, 16320, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(18) ⊂ Ce(12) [i] based on
- linear OA(4109, 16430, F4, 18) (dual of [16430, 16321, 19]-code), using Gilbert–Varšamov bound and bm = 4109 > Vbs−1(k−1) = 166700 027010 536656 823869 781104 264101 530933 870761 148571 702420 458896 [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(4109, 16429, F4, 19) (dual of [16429, 16320, 20]-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(4110, 5476, F4, 21, 19) (dual of [(5476, 21), 114886, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |