Information on Result #677402
Linear OA(3133, 274, F3, 41) (dual of [274, 141, 42]-code), using construction XX applied to Ce(40) ⊂ Ce(34) ⊂ Ce(33) based on
- linear OA(3121, 243, F3, 41) (dual of [243, 122, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3106, 243, F3, 35) (dual of [243, 137, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3101, 243, F3, 34) (dual of [243, 142, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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
None.