Information on Result #673741
Linear OA(2260, 275, F2, 121) (dual of [275, 15, 122]-code), using construction XX applied to Ce(126) ⊂ Ce(118) ⊂ Ce(110) based on
- linear OA(2247, 256, F2, 127) (dual of [256, 9, 128]-code), using an extension Ce(126) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,126], and designed minimum distance d ≥ |I|+1 = 127 [i]
- linear OA(2243, 256, F2, 119) (dual of [256, 13, 120]-code), using an extension Ce(118) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,118], and designed minimum distance d ≥ |I|+1 = 119 [i]
- linear OA(2235, 256, F2, 111) (dual of [256, 21, 112]-code), using an extension Ce(110) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,110], and designed minimum distance d ≥ |I|+1 = 111 [i]
- linear OA(21, 7, F2, 1) (dual of [7, 6, 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(210, 12, F2, 7) (dual of [12, 2, 8]-code), using
- repeating each code word 4 times [i] based on linear OA(21, 3, F2, 1) (dual of [3, 2, 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 (see above)
- repeating each code word 4 times [i] based on linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-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(2260, 275, F2, 120) (dual of [275, 15, 121]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2259, 274, F2, 120) (dual of [274, 15, 121]-code) | [i] | Truncation | |
| 3 | Linear OOA(2260, 55, F2, 5, 121) (dual of [(55, 5), 15, 122]-NRT-code) | [i] | OOA Folding | |