Commentaire sur Menachot 10:5

שלא ברצון חכמים – that he decreed that lest one eats from the new crop (i.e., grain that ripened before Passover. The Torah prohibits harvesting and eating this produce until after the Omer offering on the 16th of Nisan) when they reap prior to offering up the Omer sacrifice, and this is already certain flour that has been harvested prior to the Omer.

After the omer was offered they used to go out and find the market of Jerusalem already full of flour and parched grain [of the new produce]; This was without the approval of the rabbis, the words of Rabbi Meir. Rabbi Judah says: it was with the approval of the rabbis.
After the omer was offered the new grain was permitted immediately, but for those that lived far off it was permitted only after midday.
After the Temple was destroyed Rabbi Yohanan ben Zakkai decreed that it should be forbidden throughout the day of the waving.
Rabbi Judah said: is it not so forbidden by the law of the Torah, for it is said, “Until this very day?”
Why was it permitted for those that lived far away from midday? Because they know that the court would not be negligent with it.
Leviticus 23:14 states, “Until that very day, until you have brought the offering for your God, you shall eat no bread or parched grain or fresh ears [of the new crop].” Our mishnah discusses when people can begin to eat of the new crop of grain.
Section one: The mishnah describes the markets of Jerusalem as being full of grain from the new crop, immediately after the omer was offered. It is easy to imagine the merchants waiting and waiting until finally they could begin selling this new grain.
The debate between Rabbi Meir and Rabbi Judah was over whether the rabbis approved of this. Rabbi Meir says they disapproved of the practice because if the merchants were already selling the new grain so quickly, it is clear that they had harvested it and ground it before the omer was offered. The fear was that they might also end up eating it before the omer. Therefore, the rabbis disapproved of this practice, although they did not successfully stop it. Rabbi Judah says that they were not concerned lest people eat it before it was permitted.
Section two: As stated above, after the omer was offered, it was permitted for people to eat the new grain. People who lived far away from the Temple could not know when the omer was offered, so they must wait until half the day had passed to begin to eat of the new harvest. Below, in section five, the mishnah explains that they do not have to wait until they have actually heard that the court offered the omer because they can assume that the court would make sure that the omer was offered by this time.
Section three: After the Temple was destroyed, Rabban Yohanan ben Zakkai forbade eating the new harvest for the entire day of the 16th of Nissan. This day is called “the day of waving” because that is when the omer was waved. It seems that Rabban Yohanan ben Zakkai reasoned that when no omer could be offered, it would be legal to eat the new harvest immediately when the day began. However, if we allowed such a practice people might forget that at one point it had been forbidden to eat until the omer was offered. Therefore, he was overly stringent and forbade people to eat for the whole day.
Rabbi Judah says that there was no need for such a “takkanah” a rabbinic ordinance. The Torah itself says that the new harvest is forbidden until “that very day.” To Rabbi Judah this clause refers to a time when there is no Temple. When there is a Temple, the new harvest is forbidden until “you have brought the offering,” the second clause of the verse. Since the Torah already encompasses instructions as to how to act in the absence of the Temple, there was no need for rabbinic legislation.

ר' יהודה אומר ברצון חכמים – that they did not decree lest he eats when he harvests/reaps. And the Halakha is according to Rabbi Yehuda.

והרחוקים – that do not know if the Omer was yet offered.

מותרים מחצו היום ולהלן – as its reason will be taught further on.

שיהא יום הנף – the sixteenth of Nisan that on it they would wave the Omer (see also Tractate Rosh Hashanah, Chapter Four, Mishnah Three and also Tractate Sukkah, Chapter 3, Mishnah 12).

כולו אסור – to eat on it the new crop.

אמר ר' יהודה – to the Tanna of our Mishnah, for Rabban Yohanan [ben Zakkai] ordained/established the practice.