MinT - Information on Result #896731

Information on Result #896731

Linear OOA(8¹⁴⁴, 16431, F₈, 2, 28) (dual of [(16431, 2), 32718, 29]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8²³, 45, F₈, 2, 14) (dual of [(45, 2), 67, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,75P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
  - an explicitly constructive algebraic function field [i]
linear OOA(8¹²¹, 16386, F₈, 2, 28) (dual of [(16386, 2), 32651, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8¹²¹, 32772, F₈, 28) (dual of [32772, 32651, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹²¹, 32773, F₈, 28) (dual of [32773, 32652, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(26) [i] based on
      1. linear OA(8¹²¹, 32768, F₈, 28) (dual of [32768, 32647, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(8¹¹⁶, 32768, F₈, 27) (dual of [32768, 32652, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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(8¹⁴⁴, 2347, F₈, 30, 28) (dual of [(2347, 30), 70266, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row