MinT - Information on Result #1115624

Information on Result #1115624

Linear OOA(2²²⁶, 3355700, F₂, 5, 12) (dual of [(3355700, 5), 16778274, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁴, 2097149, F₂, 5, 6) (dual of [(2097149, 5), 10485681, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁴, 2097150, F₂, 3, 6) (dual of [(2097150, 3), 6291386, 7]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
linear OOA(2¹⁶², 1677850, F₂, 5, 12) (dual of [(1677850, 5), 8389088, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁴, 130, F₂, 5, 6) (dual of [(130, 5), 626, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2³, 3, F₂, 5, 3) (dual of [(3, 5), 12, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(5;12,2) [i]
      2. linear OOA(2²¹, 127, F₂, 5, 6) (dual of [(127, 5), 614, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹³⁸, 1677720, F₂, 5, 12) (dual of [(1677720, 5), 8388462, 13]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.