MinT - Information on Result #1012018

Information on Result #1012018

Linear OOA(4¹¹², 5480, F₄, 3, 19) (dual of [(5480, 3), 16328, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹², 14, F₄, 3, 9) (dual of [(14, 3), 30, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,32P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4¹⁰⁰, 5466, F₄, 3, 19) (dual of [(5466, 3), 16298, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4¹⁰⁰, 16398, F₄, 19) (dual of [16398, 16298, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁰⁰, 16400, F₄, 19) (dual of [16400, 16300, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(4⁹⁹, 16385, F₄, 19) (dual of [16385, 16286, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 4¹⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      2. linear OA(4⁸⁵, 16385, F₄, 17) (dual of [16385, 16300, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 4¹⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      3. linear OA(4¹, 15, F₄, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹¹², 1826, F₄, 21, 19) (dual of [(1826, 21), 38234, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row