Information on Result #894491
Linear OOA(2243, 4194437, F2, 2, 19) (dual of [(4194437, 2), 8388631, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(235, 136, F2, 2, 9) (dual of [(136, 2), 237, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(235, 272, F2, 9) (dual of [272, 237, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(235, 273, F2, 9) (dual of [273, 238, 10]-code), using
- construction XX applied to C1 = C([253,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([253,6]) [i] based on
- linear OA(225, 255, F2, 7) (dual of [255, 230, 8]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(225, 255, F2, 7) (dual of [255, 230, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(233, 255, F2, 9) (dual of [255, 222, 10]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(217, 255, F2, 5) (dual of [255, 238, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code) (see above)
- construction XX applied to C1 = C([253,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([253,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(235, 273, F2, 9) (dual of [273, 238, 10]-code), using
- OOA 2-folding [i] based on linear OA(235, 272, F2, 9) (dual of [272, 237, 10]-code), using
- linear OOA(2208, 4194301, F2, 2, 19) (dual of [(4194301, 2), 8388394, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2208, 8388602, F2, 19) (dual of [8388602, 8388394, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 2-folding [i] based on linear OA(2208, 8388602, F2, 19) (dual of [8388602, 8388394, 20]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2243, 2097218, F2, 4, 19) (dual of [(2097218, 4), 8388629, 20]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2243, 1048609, F2, 8, 19) (dual of [(1048609, 8), 8388629, 20]-NRT-code) | [i] | ||