Information on Result #2960863
Linear OOA(2238, 299597, F2, 7, 23) (dual of [(299597, 7), 2096941, 24]-NRT-code), using 21 times duplication based on linear OOA(2237, 299597, F2, 7, 23) (dual of [(299597, 7), 2096942, 24]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2237, 2097179, F2, 23) (dual of [2097179, 2096942, 24]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2234, 2097176, F2, 23) (dual of [2097176, 2096942, 24]-code), using
- adding a parity check bit [i] based on linear OA(2233, 2097175, F2, 22) (dual of [2097175, 2096942, 23]-code), using
- construction X4 applied to C([0,22]) ⊂ C([1,20]) [i] based on
- linear OA(2232, 2097151, F2, 23) (dual of [2097151, 2096919, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2210, 2097151, F2, 20) (dual of [2097151, 2096941, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
- dual of repetition code with length 24 [i]
- linear OA(21, 24, F2, 1) (dual of [24, 23, 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
- construction X4 applied to C([0,22]) ⊂ C([1,20]) [i] based on
- adding a parity check bit [i] based on linear OA(2233, 2097175, F2, 22) (dual of [2097175, 2096942, 23]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2234, 2097176, F2, 23) (dual of [2097176, 2096942, 24]-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 OOA(2238, 277712, F2, 8, 23) (dual of [(277712, 8), 2221458, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (215, 238, 277712)-net over F2 | [i] | ||