Researchers are looking for a better way to prevent an ischemic stroke which occurs when a blood clot travelled to the brain in people who within the last 72 hours had: * an acute stroke due to a blood clot that formed outside the heart (acute non-cardioembolic ischemic stroke), or * TIA/mini-stroke with a high risk of turning into a stroke (high-risk transient ischemic attack), and who are planned to receive standard of care therapy. Acute ischemic strokes or TIA/mini-stroke result from a blocked or reduced blood flow to a part of the brain. They are caused by blood clots that travel to the brain and block the vessels that supply it. If these blood clots form elsewhere than in the heart, the stroke is called non-cardioembolic. People who already had a non-cardioembolic stroke are more likely to have another stroke. This is why they are treated preventively with an antiplatelet therapy, the current standard of care. Antiplatelet medicines prevent platelets, components of blood clotting, from clumping together. Anticoagulants are another type of medicine that prevents blood clots from forming by interfering with a process known as coagulation (or blood clotting). The study treatment asundexian is a new type of anticoagulant currently under development to provide further treatment options. Asundexian aims to further improve the standard of care without increasing the risk of bleeding. The main purpose of this study is to learn whether asundexian works better than placebo at reducing ischemic strokes in participants who recently had a non-cardioembolic ischemic stroke or TIA/mini-stroke when given in addition to standard antiplatelet therapy. A placebo is a treatment that looks like a medicine but does not have any medicine in it. Another aim is to compare the occurrence of major bleeding events during the study between the asundexian and the placebo group. Major bleedings have a serious or even life-threatening impact on a person's health. Dependent on the treatment group, the participants will either take asundexian or placebo once a day for at least 3 months up to 31 months. Approximately every 3 months during the treatment period, either a phone call or a visit to the study site is scheduled on an alternating basis. In addition, one visit before and up to two visits after the treatment period are planned. During the study, the study team will: * Check vital signs such as blood pressure and heart rate * Examine the participants' heart health using an electrocardiogram (ECG) * Take blood samples * Ask the participants questions about how they are feeling and what adverse events they are having. An adverse event is any medical problem that a participant has during a study. Doctors keep track of all adverse events that happen in studies, even if they do not think the adverse events might be related to the study treatments. In addition, the participants will be asked to complete a questionnaire on quality of life at certain time points during the study.