Information on Result #713321
Linear OA(756, 372, F7, 18) (dual of [372, 316, 19]-code), using construction XX applied to C1 = C([335,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([335,10]) based on
- linear OA(743, 342, F7, 17) (dual of [342, 299, 18]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−7,−6,…,9}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(728, 342, F7, 11) (dual of [342, 314, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(746, 342, F7, 18) (dual of [342, 296, 19]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−7,−6,…,10}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(710, 27, F7, 6) (dual of [27, 17, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(710, 25, F7, 6) (dual of [25, 15, 7]-code), using an extension Ce(5) of the narrow-sense BCH-code C(I) with length 24 | 72−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(78, 25, F7, 5) (dual of [25, 17, 6]-code), using an extension Ce(4) of the narrow-sense BCH-code C(I) with length 24 | 72−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 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.