Information on Result #1434201
Linear OOA(4246, 16441, F4, 2, 44) (dual of [(16441, 2), 32636, 45]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4246, 16441, F4, 44) (dual of [16441, 16195, 45]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4245, 16439, F4, 44) (dual of [16439, 16194, 45]-code), using
- construction X applied to Ce(44) ⊂ Ce(36) [i] based on
- linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- 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(413, 55, F4, 6) (dual of [55, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(44) ⊂ Ce(36) [i] based on
- linear OA(4245, 16440, F4, 43) (dual of [16440, 16195, 44]-code), using Gilbert–Varšamov bound and bm = 4245 > Vbs−1(k−1) = 86 255439 833587 769115 546280 187470 614841 074447 503624 857998 096348 267507 577990 581222 545492 634860 194345 453600 888024 467279 216903 315092 704224 773718 491482 [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(4245, 16439, F4, 44) (dual of [16439, 16194, 45]-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(4246, 8220, F4, 3, 44) (dual of [(8220, 3), 24414, 45]-NRT-code) | [i] | OOA Folding | |