MinT - Information on Result #1118744

Information on Result #1118744

Linear OOA(256⁵⁷, 3355956, F₂₅₆, 5, 12) (dual of [(3355956, 5), 16779723, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹⁶, 2796201, F₂₅₆, 5, 6) (dual of [(2796201, 5), 13980989, 7]-NRT-code), using
- OA 3-folding and stacking [i] 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]
linear OOA(256⁴¹, 1677978, F₂₅₆, 5, 12) (dual of [(1677978, 5), 8389849, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256⁷, 258, F₂₅₆, 5, 6) (dual of [(258, 5), 1283, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 7, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. linear OOA(256³⁴, 1677720, F₂₅₆, 5, 12) (dual of [(1677720, 5), 8388566, 13]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(256³⁴, 8388600, F₂₅₆, 12) (dual of [8388600, 8388566, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(256³⁴, large, F₂₅₆, 12) (dual of [large, large−34, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

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