CAMBRIDGE, Mass. Dozens of Harvard University students are being investigated for cheating after school officials discovered they may have shared answers or plagiarized on a final exam.

Harvard officials declined to release the name of the class, the students’ names or the exact number being investigated, citing privacy laws.

The undergraduate class had a minimum of 250 students and possible cheating was discovered in roughly half the take-home exams, university officials said Thursday.

“These allegations, if proven, represent totally unacceptable behavior that betrays the trust upon which intellectual inquiry at Harvard depends,” President Drew Faust said.

Each student whose work is in question has been called to appear before a subcommittee of the Harvard College Administrative Board, which reviews issues of academic integrity, said Jay M. Harris, dean of undergraduate Education. He emphasized that none of the allegations have been proven and said there’s no evidence of widespread cheating at Harvard.

“The facts that are before us are that we have a problem in this one course,” Harris said. “I hope that doesn’t sound overly naive, I don’t want to be naive, but this is what we have. The rest would be speculation.

“Looking at the students we have and the work that they do, I would be loathe to say this is something that represents Harvard students generally.”

The spring course included undergraduates at all class levels, Harris said. A teaching assistant noticed some possible problems on the tests, including evidence that students collaborated on answers or used the same long, identical strings of words. The exam had clear instructions that no collaboration was allowed, Harris said.

The assistant notified the professor, who referred the case in May to the administrative board. After interviewing some students, the board found what Harris characterized as “cause for concern.”

Depending on the offense, the punishments range from an admonition, a sort of warning for a first offense, to being forced to withdraw from Harvard for a year. It wasn’t immediately clear what sanctions any student who has graduated may face.

There’s no timeline for when the investigation will be finished, Harris said.

“We believe in due process for students and fairness,” he said. “Everyone wants it done yesterday, but we have to be patient. It’s going to take as long as it takes.”

A Harvard spokesman said he knows of no incidents in recent memory of possible cheating at the university on this scale.

In response to the allegations, a Harvard committee on academic integrity led by Harris will present recommendations on how to enforce faculty-wide expectations of academic honesty.

In an email Thursday, Michael D. Smith, dean of the Faculty of Arts and Sciences, urged faculty members to clarify policies on student collaboration and work to “foster a culture of honesty and integrity.”

The school plans to initiate broad conversations on campus about academic honesty, including why it’s vital to intellectual inquiry. It is also considering instituting an honor code. Such codes at other schools, for instance, set standards for honesty and require students to sign completed work, attesting that they followed those standards.

“We really think we need to work harder,” Harris said. “We do think it’s an opportunity to really put out before the community how much we value integrity.”