Information on Result #678249
Linear OA(4181, 1048636, F4, 23) (dual of [1048636, 1048455, 24]-code), using construction X applied to Ce(22) ⊂ Ce(16) based on
- linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(410, 60, F4, 5) (dual of [60, 50, 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
Mode: Constructive and 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 OA(4182, 1048637, F4, 23) (dual of [1048637, 1048455, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4183, 1048638, F4, 23) (dual of [1048638, 1048455, 24]-code) | [i] | ||
| 3 | Linear OA(4184, 1048639, F4, 23) (dual of [1048639, 1048455, 24]-code) | [i] | ||
| 4 | Linear OA(4185, 1048640, F4, 23) (dual of [1048640, 1048455, 24]-code) | [i] | ||
| 5 | Linear OA(4186, 1048641, F4, 23) (dual of [1048641, 1048455, 24]-code) | [i] | ||
| 6 | Linear OA(4184, 1048640, F4, 23) (dual of [1048640, 1048456, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(4185, 1048642, F4, 23) (dual of [1048642, 1048457, 24]-code) | [i] | ||
| 8 | Linear OA(4186, 1048644, F4, 23) (dual of [1048644, 1048458, 24]-code) | [i] | ||
| 9 | Linear OOA(4181, 524318, F4, 2, 23) (dual of [(524318, 2), 1048455, 24]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(4181, 349545, F4, 3, 23) (dual of [(349545, 3), 1048454, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(4181, 95330, F4, 23, 23) (dual of [(95330, 23), 2192409, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |