Information on Result #1428641
Linear OOA(4201, 15672, F4, 2, 36) (dual of [(15672, 2), 31143, 37]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4201, 15672, F4, 36) (dual of [15672, 15471, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4201, 16430, F4, 36) (dual of [16430, 16229, 37]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4200, 16429, F4, 36) (dual of [16429, 16229, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(29) [i] based on
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4155, 16384, F4, 30) (dual of [16384, 16229, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(36) ⊂ Ce(29) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4200, 16429, F4, 36) (dual of [16429, 16229, 37]-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(4201, 7836, F4, 3, 36) (dual of [(7836, 3), 23307, 37]-NRT-code) | [i] | OOA Folding |