MinT - Information on Result #1014705

Information on Result #1014705

Linear OOA(8⁸⁷, 10941, F₈, 3, 18) (dual of [(10941, 3), 32736, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹¹, 17, F₈, 3, 9) (dual of [(17, 3), 40, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,41P) [i] based on function field F/F₈ with g(F) = 2 and N(F) ≥ 17, using
  - a function field by SÃ©mirat [i]
linear OOA(8⁷⁶, 10924, F₈, 3, 18) (dual of [(10924, 3), 32696, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8⁷⁶, 32772, F₈, 18) (dual of [32772, 32696, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁷⁶, 32773, F₈, 18) (dual of [32773, 32697, 19]-code), using
    - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
      1. linear OA(8⁷⁶, 32768, F₈, 18) (dual of [32768, 32692, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. linear OA(8⁷¹, 32768, F₈, 17) (dual of [32768, 32697, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(8⁰, 5, F₈, 0) (dual of [5, 5, 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, 3646, F₈, 21, 18) (dual of [(3646, 21), 76479, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row