Reference for Sukkah 1:1
סֻכָּה שֶׁהִיא גְבוֹהָה לְמַעְלָה מֵעֶשְׂרִים אַמָּה, פְּסוּלָה. רַבִּי יְהוּדָה מַכְשִׁיר. וְשֶׁאֵינָהּ גְּבוֹהָה עֲשָׂרָה טְפָחִים, וְשֶׁאֵין לָהּ שְׁלֹשָׁה דְּפָנוֹת, וְשֶׁחַמָּתָהּ מְרֻבָּה מִצִּלָּתָהּ, פְּסוּלָה. סֻכָּה יְשָׁנָה, בֵּית שַׁמַּאי פּוֹסְלִין, וּבֵית הִלֵּל מַכְשִׁירִין. וְאֵיזוֹ הִיא סֻכָּה יְשָׁנָה, כָּל שֶׁעֲשָׂאָהּ קֹדֶם לֶחָג שְׁלשִׁים יוֹם. אֲבָל אִם עֲשָׂאָהּ לְשֵׁם חָג, אֲפִלּוּ מִתְּחִלַּת הַשָּׁנָה, כְּשֵׁרָה:
A succah that is higher than twenty cubits is pasul (unfit), [for a succah must be a temporary dwelling, it being written (Deuteronomy 16:13): "The festival of succoth shall you make for yourself for seven days." The Torah hereby says: Make a succah (to last) for (a period of) seven days. And above twenty cubits, one does not make a temporary dwelling, but a permanent one.] R. Yehudah rules it kasher, [holding that a succah must be a permanent dwelling. The halachah is not in accordance with R. Yehudah.] And the following are unfit: one that is less than twenty handbreadths, [this being a fetid dwelling, and one does not live in a fetid dwelling.], one lacking three walls, [it being written (Leviticus 23:42): "In succoth," "in succoth," "in succoth," two defective (without the vav) and one plene (with the vav, having the effect of two): one, for the schach (the covering of the succah), the meaning of "succah" being "schach," leaving us with three, for three walls. A halachah to Moses on Sinai "comes and reduces one wall," setting it at a handbreadth. So that we are left with two of regulation size, and one, even a handbreadth. Therefore, if a succah has two walls, one next to the other, a third wall is made of somewhat more than a handbreadth and placed less than three handbreadths away from one of the two walls. For anything less than three handbreadths away from something is considered as joined to it (lavud), so that it (the third wall) is considered as one of four handbreadths, so that most of the wall is made and we have a succah of three walls, to which the form of an entrance must be added. And if the two walls are opposite each other, with an empty space in between, a board somewhat more than four handbreadths is brought and stood less than three handbreadths away from one of the two walls, so that the board is considered to be one of seven cubits, which is the (required) size for the kashruth of a succah in length and width, a succah needing to be seven by seven in order to contain one's head and most of his body and his table — six by six for his head and most of his body, and one by one for his table.], and one whose sun is more than its shade. [But if they are equal, it is kasher, And this is so only when they are equal below, on the ground of the succah, in which instance it is certain that above, in the schach, the shade is greater than the sun, as people say: "A zuz above is an astira (half a zuz) below."] An old succah — Beth Shammai rule it pasul, and Beth Hillel rule it kasher. What is "an old succah"? One which was made thirty days before the festival. But if it were made for the sake of the festival, even from the beginning of the year, it is kasher. [Beth Shammai rule it pasul, for they require a succah lishmah (for the sake of the mitzvah); but this one was made without such intent. But if it were made within thirty days of the festival, since in that period people review the halachoth of the festival, it is assumed that it was made lishmah. Before thirty days, it is assumed otherwise. And Beth Hillel rule it kasher, for they do not require a succah (to be made) for the sake of the festival.]