Information on Result #1541623
Linear OOA(4204, 176531, F4, 3, 28) (dual of [(176531, 3), 529389, 29]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4204, 176531, F4, 28) (dual of [176531, 176327, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(4204, 262212, F4, 28) (dual of [262212, 262008, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4203, 262211, F4, 28) (dual of [262211, 262008, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(413, 67, F4, 6) (dual of [67, 54, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(413, 64, F4, 6) (dual of [64, 51, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(40, 3, F4, 0) (dual of [3, 3, 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
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4203, 262211, F4, 28) (dual of [262211, 262008, 29]-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(4204, 35306, F4, 33, 28) (dual of [(35306, 33), 1164894, 29]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |