MinT - Information on Result #735468

Information on Result #735468

Linear OA(81⁴⁰, 538007, F₈₁, 11) (dual of [538007, 537967, 12]-code), using (u,Â u+v)-construction based on

linear OA(81⁹, 6563, F₈₁, 5) (dual of [6563, 6554, 6]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(81², 82, F₈₁, 2) (dual of [82, 80, 3]-code or 82-arc in PG(1,81)), using
    - extended Reedâ€“Solomon code RS_e(80,81) [i]
    - Hamming code H(2,81) [i]
  2. linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
    - a code by Danev and Olsson [i]
linear OA(81³¹, 531444, F₈₁, 11) (dual of [531444, 531413, 12]-code), using
- constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
  1. linear OA(81³¹, 531441, F₈₁, 11) (dual of [531441, 531410, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  2. linear OA(81²⁸, 531441, F₈₁, 10) (dual of [531441, 531413, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
  3. linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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(81⁴⁰, 269003, F₈₁, 2, 11) (dual of [(269003, 2), 537966, 12]-NRT-code)	[i]		OOA Folding
2	Linear OOA(81⁴⁰, 107601, F₈₁, 11, 11) (dual of [(107601, 11), 1183571, 12]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row