MinT - Information on Result #1014758

Information on Result #1014758

Linear OOA(8¹⁰⁸, 87400, F₈, 3, 19) (dual of [(87400, 3), 262092, 20]-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(8⁹⁷, 87383, F₈, 3, 19) (dual of [(87383, 3), 262052, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8⁹⁷, 262149, F₈, 19) (dual of [262149, 262052, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁹⁷, 262150, F₈, 19) (dual of [262150, 262053, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
      1. linear OA(8⁹⁷, 262144, F₈, 19) (dual of [262144, 262047, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(8⁹¹, 262144, F₈, 18) (dual of [262144, 262053, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      3. linear OA(8⁰, 6, F₈, 0) (dual of [6, 6, 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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁰⁸, 29133, F₈, 21, 19) (dual of [(29133, 21), 611685, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row