MinT - Information on Result #1014459

Information on Result #1014459

Linear OOA(8⁸⁷, 699077, F₈, 3, 13) (dual of [(699077, 3), 2097144, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁹, 24, F₈, 3, 6) (dual of [(24, 3), 63, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,65P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8⁷⁸, 699053, F₈, 3, 13) (dual of [(699053, 3), 2097081, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8⁷⁸, 2097159, F₈, 13) (dual of [2097159, 2097081, 14]-code), using
  - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
    1. linear OA(8⁷⁸, 2097152, F₈, 13) (dual of [2097152, 2097074, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(8⁷¹, 2097152, F₈, 12) (dual of [2097152, 2097081, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    3. linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8⁸⁷, 349538, F₈, 15, 13) (dual of [(349538, 15), 5242983, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row