Information on Result #612498
Linear OA(3116, 121, F3, 80) (dual of [121, 5, 81]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,75], and minimum distance d ≥ |{5,15,25,…,−52}|+1 = 81 (BCH-bound)
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3116, 121, F3, 79) (dual of [121, 5, 80]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3117, 122, F3, 80) (dual of [122, 5, 81]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(3115, 120, F3, 79) (dual of [120, 5, 80]-code) | [i] | Truncation | |
| 4 | Linear OA(3114, 119, F3, 78) (dual of [119, 5, 79]-code) | [i] | ||
| 5 | Linear OA(3113, 118, F3, 77) (dual of [118, 5, 78]-code) | [i] | ||
| 6 | Linear OA(3111, 116, F3, 75) (dual of [116, 5, 76]-code) | [i] | ||
| 7 | Linear OA(3110, 115, F3, 74) (dual of [115, 5, 75]-code) | [i] | ||
| 8 | Linear OA(3109, 114, F3, 73) (dual of [114, 5, 74]-code) | [i] | ||
| 9 | Linear OA(3237, 242, F3, 161) (dual of [242, 5, 162]-code) | [i] | Repeating Each Code Word | |
| 10 | Linear OA(3121, 126, F3, 81) (dual of [126, 5, 82]-code) | [i] | Juxtaposition | |
| 11 | Linear OA(3122, 127, F3, 82) (dual of [127, 5, 83]-code) | [i] | ||
| 12 | Linear OA(3124, 129, F3, 83) (dual of [129, 5, 84]-code) | [i] | ||
| 13 | Linear OA(3125, 130, F3, 84) (dual of [130, 5, 85]-code) | [i] | ||
| 14 | Linear OA(3126, 131, F3, 85) (dual of [131, 5, 86]-code) | [i] | ||
| 15 | Linear OA(3127, 132, F3, 86) (dual of [132, 5, 87]-code) | [i] | ||
| 16 | Linear OA(3131, 136, F3, 87) (dual of [136, 5, 88]-code) | [i] | ||
| 17 | Linear OA(3132, 137, F3, 88) (dual of [137, 5, 89]-code) | [i] | ||
| 18 | Linear OA(3133, 138, F3, 89) (dual of [138, 5, 90]-code) | [i] | ||
| 19 | Linear OA(3135, 140, F3, 90) (dual of [140, 5, 91]-code) | [i] | ||
| 20 | Linear OA(3136, 141, F3, 91) (dual of [141, 5, 92]-code) | [i] | ||
| 21 | Linear OA(3137, 142, F3, 92) (dual of [142, 5, 93]-code) | [i] | ||
| 22 | Linear OA(3139, 144, F3, 93) (dual of [144, 5, 94]-code) | [i] | ||
| 23 | Linear OA(3140, 145, F3, 94) (dual of [145, 5, 95]-code) | [i] | ||
| 24 | Linear OA(3141, 146, F3, 95) (dual of [146, 5, 96]-code) | [i] | ||
| 25 | Linear OA(3134, 139, F3, 90) (dual of [139, 5, 91]-code) | [i] | ||
| 26 | Linear OA(3135, 140, F3, 91) (dual of [140, 5, 92]-code) | [i] | ||
| 27 | Linear OA(3136, 141, F3, 92) (dual of [141, 5, 93]-code) | [i] | ||
| 28 | Linear OA(3120, 126, F3, 80) (dual of [126, 6, 81]-code) | [i] | ✔ | Construction X with Cyclic Codes |
| 29 | Linear OA(3136, 149, F3, 77) (dual of [149, 13, 78]-code) | [i] | ✔ | |
| 30 | Linear OA(3128, 143, F3, 71) (dual of [143, 15, 72]-code) | [i] | ✔ | |
| 31 | Linear OA(3129, 145, F3, 71) (dual of [145, 16, 72]-code) | [i] | ✔ | Construction XX with Cyclic Codes |
| 32 | Linear OA(3137, 151, F3, 77) (dual of [151, 14, 78]-code) | [i] | ✔ | |
| 33 | Linear OA(3132, 148, F3, 72) (dual of [148, 16, 73]-code) | [i] | ✔ | |
| 34 | Linear OA(3127, 143, F3, 71) (dual of [143, 16, 72]-code) | [i] | ✔ | |
| 35 | Linear OA(3131, 146, F3, 72) (dual of [146, 15, 73]-code) | [i] | ✔ | |
| 36 | Linear OA(3130, 144, F3, 72) (dual of [144, 14, 73]-code) | [i] | ✔ | |
| 37 | Linear OA(3134, 149, F3, 74) (dual of [149, 15, 75]-code) | [i] | ✔ | |
| 38 | Linear OA(3132, 147, F3, 73) (dual of [147, 15, 74]-code) | [i] | ✔ | |
| 39 | Linear OA(3130, 145, F3, 72) (dual of [145, 15, 73]-code) | [i] | ✔ | |
| 40 | Linear OA(3125, 140, F3, 71) (dual of [140, 15, 72]-code) | [i] | ✔ | |
| 41 | Linear OA(3123, 138, F3, 70) (dual of [138, 15, 71]-code) | [i] | ✔ | |
| 42 | Linear OA(3133, 147, F3, 74) (dual of [147, 14, 75]-code) | [i] | ✔ | |
| 43 | Linear OA(3131, 145, F3, 73) (dual of [145, 14, 74]-code) | [i] | ✔ | |
| 44 | Linear OA(3129, 143, F3, 72) (dual of [143, 14, 73]-code) | [i] | ✔ | |
| 45 | Linear OA(3132, 145, F3, 74) (dual of [145, 13, 75]-code) | [i] | ✔ | |
| 46 | Linear OA(3130, 143, F3, 73) (dual of [143, 13, 74]-code) | [i] | ✔ | |
| 47 | Linear OA(3128, 141, F3, 72) (dual of [141, 13, 73]-code) | [i] | ✔ | |
| 48 | Linear OA(3137, 153, F3, 75) (dual of [153, 16, 76]-code) | [i] | ✔ | |
| 49 | Linear OA(3132, 147, F3, 72) (dual of [147, 15, 73]-code) | [i] | ✔ | Construction XX with a Chain of Cyclic Codes |
| 50 | Linear OA(3140, 153, F3, 79) (dual of [153, 13, 80]-code) | [i] | ✔ | |
| 51 | Linear OA(3126, 139, F3, 70) (dual of [139, 13, 71]-code) | [i] | ✔ | |
| 52 | Linear OA(3130, 146, F3, 71) (dual of [146, 16, 72]-code) | [i] | ✔ | |
| 53 | Linear OOA(3116, 60, F3, 2, 80) (dual of [(60, 2), 4, 81]-NRT-code) | [i] | OOA Folding | |
| 54 | Linear OOA(3116, 40, F3, 3, 80) (dual of [(40, 3), 4, 81]-NRT-code) | [i] | ||
| 55 | Linear OOA(3116, 24, F3, 5, 80) (dual of [(24, 5), 4, 81]-NRT-code) | [i] | ||