Information on Result #707032
Linear OA(4152, 277, F4, 54) (dual of [277, 125, 55]-code), using construction XX applied to C1 = C([33,85]), C2 = C([41,86]), C3 = C1 + C2 = C([41,85]), and C∩ = C1 ∩ C2 = C([33,86]) based on
- linear OA(4139, 255, F4, 53) (dual of [255, 116, 54]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {33,34,…,85}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(4129, 255, F4, 46) (dual of [255, 126, 47]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {41,42,…,86}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(4143, 255, F4, 54) (dual of [255, 112, 55]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {33,34,…,86}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(4125, 255, F4, 45) (dual of [255, 130, 46]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {41,42,…,85}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(49, 18, F4, 7) (dual of [18, 9, 8]-code), using
- construction X applied to C({0,1,3}) ⊂ C({1,3}) [i] based on
- linear OA(49, 17, F4, 7) (dual of [17, 8, 8]-code), using the cyclic code C(A) with length 17 | 44−1, defining set A = {0,1,3}, and minimum distance d ≥ |{1,5}| + |{−6,−5,…,0}∖{−3}| = 8 (general Roos-bound) [i]
- linear OA(48, 17, F4, 6) (dual of [17, 9, 7]-code), using the cyclic code C(A) with length 17 | 44−1, defining set A = {1,3}, and minimum distance d ≥ |{−5,−3,−1,…,5}|+1 = 7 (BCH-bound) [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to C({0,1,3}) ⊂ C({1,3}) [i] based on
- linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
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.