MinT - Information on Result #2496019

Information on Result #2496019

Linear OOA(4²³¹, 4194542, F₄, 2, 22) (dual of [(4194542, 2), 8388853, 23]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²²⁹, 4194541, F₄, 2, 22) (dual of [(4194541, 2), 8388853, 23]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4³⁶, 240, F₄, 2, 11) (dual of [(240, 2), 444, 12]-NRT-code), using
  - extracting embedded OOA [i] based on digital (25, 36, 240)-net over F₄, using
    - trace code for nets [i] based on digital (1, 12, 80)-net over F₆₄, using
      - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
2. linear OOA(4¹⁹³, 4194301, F₄, 2, 22) (dual of [(4194301, 2), 8388409, 23]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁹³, 8388602, F₄, 22) (dual of [8388602, 8388409, 23]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁹³, large, F₄, 22) (dual of [large, large−193, 23]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(4²³², 4194542, F₄, 2, 22) (dual of [(4194542, 2), 8388852, 23]-NRT-code)	[i]		OOA Duplication