Information on Result #677421
Linear OA(3123, 274, F3, 38) (dual of [274, 151, 39]-code), using construction XX applied to Ce(37) ⊂ Ce(31) ⊂ Ce(30) based on
- linear OA(3111, 243, F3, 38) (dual of [243, 132, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(396, 243, F3, 32) (dual of [243, 147, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(391, 243, F3, 31) (dual of [243, 152, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(38, 27, F3, 5) (dual of [27, 19, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(319, 27, F3, 13) (dual of [27, 8, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- nonexistence of linear OA(318, 22, F3, 13) (dual of [22, 4, 14]-code), because
- 1 times truncation [i] would yield linear OA(317, 21, F3, 12) (dual of [21, 4, 13]-code), but
- linear OA(319, 27, F3, 13) (dual of [27, 8, 14]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(30, 4, F3, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(3123, 137, F3, 2, 38) (dual of [(137, 2), 151, 39]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3123, 91, F3, 3, 38) (dual of [(91, 3), 150, 39]-NRT-code) | [i] | ||