MinT - Information on Result #1015142

Information on Result #1015142

Linear OOA(8¹⁵⁸, 10958, F₈, 3, 31) (dual of [(10958, 3), 32716, 32]-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(8¹³⁶, 10924, F₈, 3, 31) (dual of [(10924, 3), 32636, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹³⁶, 32772, F₈, 31) (dual of [32772, 32636, 32]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹³⁶, 32773, F₈, 31) (dual of [32773, 32637, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(29) [i] based on
      1. linear OA(8¹³⁶, 32768, F₈, 31) (dual of [32768, 32632, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. 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]
      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.

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(8¹⁵⁸, 2191, F₈, 33, 31) (dual of [(2191, 33), 72145, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row