MinT - Information on Result #1014989

Information on Result #1014989

Linear OOA(8¹²⁹, 10952, F₈, 3, 26) (dual of [(10952, 3), 32727, 27]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁸, 28, F₈, 3, 13) (dual of [(28, 3), 66, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,70P) [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
  - a function field by SÃ©mirat [i]
linear OOA(8¹¹¹, 10924, F₈, 3, 26) (dual of [(10924, 3), 32661, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹¹¹, 32772, F₈, 26) (dual of [32772, 32661, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹¹¹, 32773, F₈, 26) (dual of [32773, 32662, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
      1. linear OA(8¹¹¹, 32768, F₈, 26) (dual of [32768, 32657, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(8¹⁰⁶, 32768, F₈, 25) (dual of [32768, 32662, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(8¹³⁰, 10952, F₈, 3, 26) (dual of [(10952, 3), 32726, 27]-NRT-code)	[i]		OOA Duplication