MinT - Information on Result #676434

Information on Result #676434

Linear OA(3¹³¹, 764, F₃, 31) (dual of [764, 633, 32]-code), using constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) based on

linear OA(3¹²¹, 730, F₃, 31) (dual of [730, 609, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 730Â | 3¹²âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
linear OA(3⁹⁷, 730, F₃, 25) (dual of [730, 633, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 730Â | 3¹²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
linear OA(3¹⁰, 34, F₃, 5) (dual of [34, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁰, 36, F₃, 5) (dual of [36, 26, 6]-code), using
  - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
    1. linear OA(3¹, 12, F₃, 1) (dual of [12, 11, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OA(3³, 12, F₃, 2) (dual of [12, 9, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
    3. linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
      - extended Golay code G_e(3) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹³¹, 382, F₃, 2, 31) (dual of [(382, 2), 633, 32]-NRT-code)	[i]		OOA Folding