The authorities effectively waived the ban on political parties for this week's vote by permitting candidates with known party allegiances to campaign freely.
At the time, California law permitted candidates to run in both major parties' primaries, a practice known as "cross-filing."
The other law will permit candidates who have participated in the program to receive post-election contributions to repay debt.
Federal regulations require television stations to permit political candidates to buy "reasonable" amounts of time for advertising.
General Zia, in an effort to solidify his power, had forbidden campaigning under political banners, permitting candidates to run only as independents.
This year, the board is reserving some debates for leading candidates and is permitting candidates who are not in the campaign finance program to participate.
Satellite technology, for example, permits candidates to beam a message directly to voters or to local cable television stations with no intervention from the news media.
Federal election law permits candidates to loan or contribute money to their own campaigns without limit, but that must be disclosed.
Second-best would be to permit candidates to spend 20 percent above the expenditure ceiling on fund-raising - the same formula used in Federal races.
Party rules permit candidates to request ballots for supporters but require that nonparty members initiate the requests.