Information on Result #678202
Linear OA(4126, 1048611, F4, 17) (dual of [1048611, 1048485, 18]-code), using construction X applied to Ce(16) ⊂ Ce(12) based on
- 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(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4126, 1048611, F4, 16) (dual of [1048611, 1048485, 17]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4127, 1048612, F4, 17) (dual of [1048612, 1048485, 18]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4128, 1048613, F4, 17) (dual of [1048613, 1048485, 18]-code) | [i] | ||
| 4 | Linear OA(4129, 1048614, F4, 17) (dual of [1048614, 1048485, 18]-code) | [i] | ||
| 5 | Linear OA(4130, 1048615, F4, 17) (dual of [1048615, 1048485, 18]-code) | [i] | ||
| 6 | Linear OA(4125, 1048610, F4, 16) (dual of [1048610, 1048485, 17]-code) | [i] | Truncation | |
| 7 | Linear OA(4129, 1048615, F4, 17) (dual of [1048615, 1048486, 18]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(4130, 1048617, F4, 17) (dual of [1048617, 1048487, 18]-code) | [i] | ||
| 9 | Linear OOA(4126, 524305, F4, 2, 17) (dual of [(524305, 2), 1048484, 18]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(4126, 349537, F4, 3, 17) (dual of [(349537, 3), 1048485, 18]-NRT-code) | [i] | ||
| 11 | Linear OOA(4126, 131076, F4, 17, 17) (dual of [(131076, 17), 2228166, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |