Information on Result #2726545
Linear OOA(4214, 524319, F4, 3, 27) (dual of [(524319, 3), 1572743, 28]-NRT-code), using 41 times duplication based on linear OOA(4213, 524319, F4, 3, 27) (dual of [(524319, 3), 1572744, 28]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4213, 524319, F4, 2, 27) (dual of [(524319, 2), 1048425, 28]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4211, 524318, F4, 2, 27) (dual of [(524318, 2), 1048425, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4211, 1048636, F4, 27) (dual of [1048636, 1048425, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(4201, 1048576, F4, 27) (dual of [1048576, 1048375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(410, 60, F4, 5) (dual of [60, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- OOA 2-folding [i] based on linear OA(4211, 1048636, F4, 27) (dual of [1048636, 1048425, 28]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4211, 524318, F4, 2, 27) (dual of [(524318, 2), 1048425, 28]-NRT-code), using
Mode: 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.