MinT - Information on Result #1151052

Information on Result #1151052

Linear OOA(2²⁵⁵, 2097278, F₂, 7, 15) (dual of [(2097278, 7), 14680691, 16]-NRT-code), using OOA 2-folding based on linear OOA(2²⁵⁵, 4194556, F₂, 4, 15) (dual of [(4194556, 4), 16777969, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁸, 4194302, F₂, 4, 7) (dual of [(4194302, 4), 16777140, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁶⁸, 4194303, F₂, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁸⁷, 2097278, F₂, 4, 15) (dual of [(2097278, 4), 8388925, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2²³, 127, F₂, 4, 7) (dual of [(127, 4), 485, 8]-NRT-code), using
      - extracting embedded OOA [i] based on digital (16, 23, 127)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
    2. linear OOA(2¹⁶⁴, 2097151, F₂, 4, 15) (dual of [(2097151, 4), 8388440, 16]-NRT-code), using
      - OOA 2-folding [i] based on linear OOA(2¹⁶⁴, 4194302, F₂, 2, 15) (dual of [(4194302, 2), 8388440, 16]-NRT-code), using
        1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁶², 4194301, F₂, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
        OOA 2-folding [i] based on linear OA(2¹⁶², 8388602, F₂, 15) (dual of [8388602, 8388440, 16]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.