MinT - Information on Result #1015108

Information on Result #1015108

Linear OOA(8¹⁵³, 10958, F₈, 3, 30) (dual of [(10958, 3), 32721, 31]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8²², 34, F₈, 3, 15) (dual of [(34, 3), 80, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,86P) [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
  - a function field by SÃ©mirat [i]
linear OOA(8¹³¹, 10924, F₈, 3, 30) (dual of [(10924, 3), 32641, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹³¹, 32772, F₈, 30) (dual of [32772, 32641, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹³¹, 32773, F₈, 30) (dual of [32773, 32642, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(28) [i] based on
      1. linear OA(8¹³¹, 32768, F₈, 30) (dual of [32768, 32637, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(8¹²⁶, 32768, F₈, 29) (dual of [32768, 32642, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(8¹⁵³, 2191, F₈, 33, 30) (dual of [(2191, 33), 72150, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row