Information on Result #702733
Linear OA(263, 1045, F2, 13) (dual of [1045, 982, 14]-code), using construction XX applied to C1 = C([1021,8]), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([1021,10]) based on
- linear OA(251, 1023, F2, 11) (dual of [1023, 972, 12]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(251, 1023, F2, 11) (dual of [1023, 972, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(261, 1023, F2, 13) (dual of [1023, 962, 14]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(241, 1023, F2, 9) (dual of [1023, 982, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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, 11, F2, 1) (dual of [11, 10, 2]-code) (see above)
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(262, 1044, F2, 12) (dual of [1044, 982, 13]-code) | [i] | Truncation | |
| 2 | Linear OOA(263, 522, F2, 2, 13) (dual of [(522, 2), 981, 14]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(263, 348, F2, 3, 13) (dual of [(348, 3), 981, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(263, 261, F2, 4, 13) (dual of [(261, 4), 981, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(263, 209, F2, 5, 13) (dual of [(209, 5), 982, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(263, 174, F2, 6, 13) (dual of [(174, 6), 981, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(263, 174, F2, 7, 13) (dual of [(174, 7), 1155, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 8 | Linear OOA(263, 174, F2, 8, 13) (dual of [(174, 8), 1329, 14]-NRT-code) | [i] | ||
| 9 | Linear OOA(263, 174, F2, 13, 13) (dual of [(174, 13), 2199, 14]-NRT-code) | [i] | ||