Information on Result #548307
There is no linear OA(2103, 112, F2, 52) (dual of [112, 9, 53]-code), because residual code would yield linear OA(251, 59, F2, 26) (dual of [59, 8, 27]-code), but
- adding a parity check bit [i] would yield linear OA(252, 60, F2, 27) (dual of [60, 8, 28]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
Mode: Bound (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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(2104, 113, F2, 53) (dual of [113, 9, 54]-code) | [i] | Truncation | |
| 2 | No linear OOA(2104, 112, F2, 2, 53) (dual of [(112, 2), 120, 54]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2105, 112, F2, 2, 54) (dual of [(112, 2), 119, 55]-NRT-code) | [i] | ||
| 4 | No linear OOA(2106, 112, F2, 2, 55) (dual of [(112, 2), 118, 56]-NRT-code) | [i] | ||
| 5 | No linear OOA(2108, 112, F2, 2, 57) (dual of [(112, 2), 116, 58]-NRT-code) | [i] | ||
| 6 | No linear OOA(2109, 112, F2, 2, 58) (dual of [(112, 2), 115, 59]-NRT-code) | [i] | ||
| 7 | No linear OOA(2110, 112, F2, 2, 59) (dual of [(112, 2), 114, 60]-NRT-code) | [i] | ||
| 8 | No linear OOA(2111, 112, F2, 2, 60) (dual of [(112, 2), 113, 61]-NRT-code) | [i] | ||
| 9 | No linear OOA(2112, 112, F2, 2, 61) (dual of [(112, 2), 112, 62]-NRT-code) | [i] | ||
| 10 | No linear OOA(2113, 112, F2, 2, 62) (dual of [(112, 2), 111, 63]-NRT-code) | [i] | ||
| 11 | No linear OOA(2114, 112, F2, 2, 63) (dual of [(112, 2), 110, 64]-NRT-code) | [i] | ||
| 12 | No linear OOA(2115, 112, F2, 2, 64) (dual of [(112, 2), 109, 65]-NRT-code) | [i] | ||
| 13 | No linear OOA(2116, 112, F2, 2, 65) (dual of [(112, 2), 108, 66]-NRT-code) | [i] | ||
| 14 | No linear OOA(2117, 112, F2, 2, 66) (dual of [(112, 2), 107, 67]-NRT-code) | [i] | ||
| 15 | No linear OOA(2118, 112, F2, 2, 67) (dual of [(112, 2), 106, 68]-NRT-code) | [i] | ||
| 16 | No linear OOA(2119, 112, F2, 2, 68) (dual of [(112, 2), 105, 69]-NRT-code) | [i] | ||
| 17 | No linear OOA(2120, 112, F2, 2, 69) (dual of [(112, 2), 104, 70]-NRT-code) | [i] | ||
| 18 | No linear OOA(2121, 112, F2, 2, 70) (dual of [(112, 2), 103, 71]-NRT-code) | [i] | ||
| 19 | No linear OOA(2122, 112, F2, 2, 71) (dual of [(112, 2), 102, 72]-NRT-code) | [i] | ||
| 20 | No linear OOA(2123, 112, F2, 2, 72) (dual of [(112, 2), 101, 73]-NRT-code) | [i] | ||
| 21 | No linear OOA(2124, 112, F2, 2, 73) (dual of [(112, 2), 100, 74]-NRT-code) | [i] | ||
| 22 | No linear OOA(2125, 112, F2, 2, 74) (dual of [(112, 2), 99, 75]-NRT-code) | [i] | ||
| 23 | No linear OOA(2126, 112, F2, 2, 75) (dual of [(112, 2), 98, 76]-NRT-code) | [i] | ||
| 24 | No linear OOA(2127, 112, F2, 2, 76) (dual of [(112, 2), 97, 77]-NRT-code) | [i] | ||
| 25 | No linear OOA(2128, 112, F2, 2, 77) (dual of [(112, 2), 96, 78]-NRT-code) | [i] | ||
| 26 | No linear OOA(2129, 112, F2, 2, 78) (dual of [(112, 2), 95, 79]-NRT-code) | [i] | ||
| 27 | No linear OOA(2130, 112, F2, 2, 79) (dual of [(112, 2), 94, 80]-NRT-code) | [i] | ||
| 28 | No linear OOA(2131, 112, F2, 2, 80) (dual of [(112, 2), 93, 81]-NRT-code) | [i] | ||
| 29 | No linear OOA(2132, 112, F2, 2, 81) (dual of [(112, 2), 92, 82]-NRT-code) | [i] | ||
| 30 | No linear OOA(2133, 112, F2, 2, 82) (dual of [(112, 2), 91, 83]-NRT-code) | [i] | ||
| 31 | No linear OOA(2134, 112, F2, 2, 83) (dual of [(112, 2), 90, 84]-NRT-code) | [i] | ||
| 32 | No linear OOA(2135, 112, F2, 2, 84) (dual of [(112, 2), 89, 85]-NRT-code) | [i] | ||
| 33 | No linear OOA(2136, 112, F2, 2, 85) (dual of [(112, 2), 88, 86]-NRT-code) | [i] | ||
| 34 | No linear OOA(2137, 112, F2, 2, 86) (dual of [(112, 2), 87, 87]-NRT-code) | [i] | ||
| 35 | No linear OOA(2138, 112, F2, 2, 87) (dual of [(112, 2), 86, 88]-NRT-code) | [i] | ||
| 36 | No linear OOA(2139, 112, F2, 2, 88) (dual of [(112, 2), 85, 89]-NRT-code) | [i] | ||
| 37 | No linear OOA(2140, 112, F2, 2, 89) (dual of [(112, 2), 84, 90]-NRT-code) | [i] | ||
| 38 | No linear OOA(2141, 112, F2, 2, 90) (dual of [(112, 2), 83, 91]-NRT-code) | [i] | ||
| 39 | No linear OOA(2142, 112, F2, 2, 91) (dual of [(112, 2), 82, 92]-NRT-code) | [i] | ||
| 40 | No linear OOA(2143, 112, F2, 2, 92) (dual of [(112, 2), 81, 93]-NRT-code) | [i] | ||
| 41 | No linear OOA(2144, 112, F2, 2, 93) (dual of [(112, 2), 80, 94]-NRT-code) | [i] | ||
| 42 | No linear OOA(2145, 112, F2, 2, 94) (dual of [(112, 2), 79, 95]-NRT-code) | [i] | ||
| 43 | No linear OOA(2146, 112, F2, 2, 95) (dual of [(112, 2), 78, 96]-NRT-code) | [i] | ||
| 44 | No linear OOA(2147, 112, F2, 2, 96) (dual of [(112, 2), 77, 97]-NRT-code) | [i] | ||
| 45 | No linear OOA(2103, 112, F2, 2, 52) (dual of [(112, 2), 121, 53]-NRT-code) | [i] | Depth Reduction | |
| 46 | No linear OOA(2103, 112, F2, 3, 52) (dual of [(112, 3), 233, 53]-NRT-code) | [i] | ||
| 47 | No linear OOA(2103, 112, F2, 4, 52) (dual of [(112, 4), 345, 53]-NRT-code) | [i] | ||
| 48 | No linear OOA(2103, 112, F2, 5, 52) (dual of [(112, 5), 457, 53]-NRT-code) | [i] | ||
| 49 | No linear OOA(2103, 112, F2, 6, 52) (dual of [(112, 6), 569, 53]-NRT-code) | [i] | ||
| 50 | No linear OOA(2103, 112, F2, 7, 52) (dual of [(112, 7), 681, 53]-NRT-code) | [i] | ||
| 51 | No linear OOA(2103, 112, F2, 8, 52) (dual of [(112, 8), 793, 53]-NRT-code) | [i] | ||
| 52 | No digital (51, 103, 112)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 53 | No linear OA(2207, 217, F2, 104) (dual of [217, 10, 105]-code) | [i] | Residual Code | |