Information on Result #676922
Linear OA(3242, 761, F3, 61) (dual of [761, 519, 62]-code), using construction XX applied to Ce(60) ⊂ Ce(55) ⊂ Ce(52) based on
- linear OA(3229, 729, F3, 61) (dual of [729, 500, 62]-code), using an extension Ce(60) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,60], and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(3214, 729, F3, 56) (dual of [729, 515, 57]-code), using an extension Ce(55) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,55], and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(3208, 729, F3, 53) (dual of [729, 521, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [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(31, 5, F3, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-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.