MinT - Information on Result #1014762

Information on Result #1014762

Linear OOA(8¹²⁵, 699077, F₈, 3, 19) (dual of [(699077, 3), 2097106, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹², 24, F₈, 3, 9) (dual of [(24, 3), 60, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,62P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8¹¹³, 699053, F₈, 3, 19) (dual of [(699053, 3), 2097046, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹¹³, 2097159, F₈, 19) (dual of [2097159, 2097046, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
    1. linear OA(8¹¹³, 2097152, F₈, 19) (dual of [2097152, 2097039, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(8¹⁰⁶, 2097152, F₈, 18) (dual of [2097152, 2097046, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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(8¹²⁵, 233025, F₈, 21, 19) (dual of [(233025, 21), 4893400, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row