MinT - Information on Result #2528677

Information on Result #2528677

OOA(128⁶⁸, large, S₁₂₈, 2, 13), using 128¹ times duplication based on OOA(128⁶⁷, large, S₁₂₈, 2, 13), using

3 times NRT-code embedding in larger space [i] based on OOA(128⁶¹, 8388602, S₁₂₈, 2, 13), using
- discarding parts of the base [i] based on linear OOA(256⁵³, 8388602, F₂₅₆, 2, 13) (dual of [(8388602, 2), 16777151, 14]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(256¹⁶, 4194301, F₂₅₆, 2, 6) (dual of [(4194301, 2), 8388586, 7]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(256¹⁶, 8388602, F₂₅₆, 6) (dual of [8388602, 8388586, 7]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹⁶, large, F₂₅₆, 6) (dual of [large, large−16, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OOA(256³⁷, 4194301, F₂₅₆, 2, 13) (dual of [(4194301, 2), 8388565, 14]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(256³⁷, 8388602, F₂₅₆, 13) (dual of [8388602, 8388565, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(256³⁷, large, F₂₅₆, 13) (dual of [large, large−37, 14]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

Mode: Constructive.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.