MinT - Information on Result #1118977

Information on Result #1118977

Linear OOA(256⁶¹, 13623, F₂₅₆, 5, 22) (dual of [(13623, 5), 68054, 23]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹⁸, 516, F₂₅₆, 5, 11) (dual of [(516, 5), 2562, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁶, 258, F₂₅₆, 5, 5) (dual of [(258, 5), 1284, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(256⁶, 258, F₂₅₆, 4, 5) (dual of [(258, 4), 1026, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (1, 6, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. linear OOA(256¹², 258, F₂₅₆, 5, 11) (dual of [(258, 5), 1278, 12]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 12, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)
linear OOA(256⁴³, 13107, F₂₅₆, 5, 22) (dual of [(13107, 5), 65492, 23]-NRT-code), using
- OOA 5-folding [i] based on linear OA(256⁴³, 65535, F₂₅₆, 22) (dual of [65535, 65492, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(256⁴³, 65536, F₂₅₆, 22) (dual of [65536, 65493, 23]-code), using
    - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Mode: Constructive and linear.

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