MinT - Information on Result #2224346

Information on Result #2224346

Linear OA(2²⁰⁴, 218, F₂, 96) (dual of [218, 14, 97]-code), using 1 times truncation based on linear OA(2²⁰⁵, 219, F₂, 97) (dual of [219, 14, 98]-code), using

concatenation of two codes [i] based on
1. linear OA(4⁶⁶, 73, F₄, 48) (dual of [73, 7, 49]-code), using
  - 2 times truncation [i] based on linear OA(4⁶⁸, 75, F₄, 50) (dual of [75, 7, 51]-code), using
    - constructionÂ XX applied to C₁Â =Â C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,47}), C₂Â =Â C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43}), C₃Â =Â C₁Â +Â C₂Â =Â C([0,31]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43,47}) [i] based on
      1. linear OA(4⁵⁹, 63, F₄, 46) (dual of [63, 4, 47]-code), using the primitive cyclic code C(A) with length 63Â = 4³âˆ’1, defining set AÂ =Â {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,47}, and minimum distance dÂ â‰¥ |{−4,−3,…,41}|+1Â =Â 47 (BCH-bound) [i]
      2. linear OA(4⁵⁹, 63, F₄, 46) (dual of [63, 4, 47]-code), using the primitive cyclic code C(A) with length 63Â = 4³âˆ’1, defining set AÂ =Â {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43}, and minimum distance dÂ â‰¥ |{1,6,11,…,−26}|+1Â =Â 47 (BCH-bound) [i]
      3. linear OA(4⁶², 63, F₄, 62) (dual of [63, 1, 63]-code or 63-arc in PG(61,4)), using the primitive cyclic code C(A) with length 63Â = 4³âˆ’1, defining set AÂ =Â {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43,47}, and minimum distance dÂ â‰¥ |{1,23,45,…,20}|+1Â =Â 63 (BCH-bound) [i]
      4. linear OA(4⁵⁶, 63, F₄, 42) (dual of [63, 7, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
      5. linear OA(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
        hyperoval in PG(2,Â 4) [i]
        the Hexacode [i]
      6. linear OA(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)) (see above)
2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁰⁴, 109, F₂, 2, 96) (dual of [(109, 2), 14, 97]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁰⁴, 72, F₂, 3, 96) (dual of [(72, 3), 12, 97]-NRT-code)	[i]		OOA Folding