MinT - Information on Result #1118958

Information on Result #1118958

Linear OOA(256⁵⁷, 13622, F₂₅₆, 5, 21) (dual of [(13622, 5), 68053, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹⁶, 515, F₂₅₆, 5, 10) (dual of [(515, 5), 2559, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁵, 257, F₂₅₆, 5, 5) (dual of [(257, 5), 1280, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(5;1280,256) [i]
  2. linear OOA(256¹¹, 258, F₂₅₆, 5, 10) (dual of [(258, 5), 1279, 11]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 11, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
linear OOA(256⁴¹, 13107, F₂₅₆, 5, 21) (dual of [(13107, 5), 65494, 22]-NRT-code), using
- OOA 5-folding [i] based on linear OA(256⁴¹, 65535, F₂₅₆, 21) (dual of [65535, 65494, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁴¹, 65536, F₂₅₆, 21) (dual of [65536, 65495, 22]-code), using
    - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Mode: Constructive and linear.

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