MinT - Information on Result #909609

Information on Result #909609

Linear OOA(4¹⁶⁹, 88, F₄, 2, 123) (dual of [(88, 2), 7, 124]-NRT-code), using juxtaposition based on

linear OOA(4⁵⁷, 32, F₄, 2, 43) (dual of [(32, 2), 7, 44]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4⁵⁷, 64, F₄, 43) (dual of [64, 7, 44]-code), using
  - an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
linear OOA(4¹⁰⁵, 56, F₄, 2, 79) (dual of [(56, 2), 7, 80]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4²², 14, F₄, 2, 19) (dual of [(14, 2), 6, 20]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4²⁷, 14, F₄, 2, 26) (dual of [(14, 2), 1, 27]-NRT-code), using
    - strength reduction [i] based on linear OOA(4²⁷, 14, F₄, 2, 27) (dual of [(14, 2), 1, 28]-NRT-code), using
      - dual of repetition NRT-code with length 14 [i]
  3. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code) (see above)

Mode: Constructive and linear.

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