Dixon was convicted on Friday of murdering James Te Aute and of severely injuring two women with a samurai sword.
The trial was Dixon's second on most of the charges relating to the 2003 attack.
The first guilty verdict was overturned by the Court of Appeal. He has already served five years.
The reasons for the retrial were released on Monday.
The Court of Appeal quashed the original convictions because it agreed with Dixon's lawyers that the judge had wrongly directed the jury on some key points.
It says Justice Potter did not correctly address the issues of insanity and intoxication and she should have directed the jury to consider the alternative charge of manslaughter.
New appeal planned
Antonie Dixon plans to appeal against the convictions for murder and intentional injury.
Lawyer Barry Hart said on Friday there are substantial grounds for another appeal because of deficiencies in summing up by the judge.
Justice Williams took almost four hours to sum up the complex legal arguments, with much of that time being spent telling the jury how to consider the issue of insanity.
Outside court, crown prosecutor Simon Moore said Justice Williams did an extraordinary job, and said it was the toughest summing up that would confront any judge in this country.
On Friday night, the jury of six men and five women in the High Court at Auckland returned its verdict after more than a day of deliberations.
Dixon, 40, was accused of eight charges after he went on a violent drug-fuelled rampage from the rural settlement of Pipiroa near Thames to Auckland.
The jury also found him guilty of kidnapping, illegally using a firearm, and breaking and entering.
Dixon stood quietly in the dock as the verdict was read out, looking down at his feet.
The defence had argued that Dixon was insane on the day of the attacks, but the Crown says he carried out intentional and calculated crimes.
By finding him guilty, the jury accepted that Dixon was not insane and that he intended to fatally shoot James Te Aute - a stranger whom he had encountered in Auckland.