Information on Result #677759
Linear OA(3108, 115, F3, 70) (dual of [115, 7, 71]-code), using construction XX applied to Ce(79) ⊂ Ce(52) ⊂ Ce(49) based on
- linear OA(380, 81, F3, 80) (dual of [81, 1, 81]-code or 81-arc in PG(79,3)), using an extension Ce(79) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
- linear OA(376, 81, F3, 53) (dual of [81, 5, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(374, 81, F3, 50) (dual of [81, 7, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(324, 30, F3, 16) (dual of [30, 6, 17]-code), using
- residual code [i] based on linear OA(374, 81, F3, 50) (dual of [81, 7, 51]-code) (see above)
- linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
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
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3108, 115, F3, 69) (dual of [115, 7, 70]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3134, 141, F3, 84) (dual of [141, 7, 85]-code) | [i] | Juxtaposition | |
| 3 | Linear OA(3135, 142, F3, 85) (dual of [142, 7, 86]-code) | [i] | ||
| 4 | Linear OOA(3108, 23, F3, 5, 70) (dual of [(23, 5), 7, 71]-NRT-code) | [i] | OOA Folding | |