I am reading an old report on the weight distribution of BCH codes, written by Tadao Kasami. The link to the report can be found here https://www.ideals.illinois.edu/items/100343/bitstreams/320511/stream
I am also attaching the images of the paper where I have difficulty understanding the content.
Now, if you can see the attached image, you will find two pages. Go to the first page, and look for the mathematical equation I have highlighted with yellow color. You will find this equation $h_i(\alpha^{- 2^{\mu_i}- 1}) = 0$. But, my reasoning says that the aforementioned equation should look this $h_i(\alpha^{ (-2)^{\mu_i}- 1}) = 0$. What do you say, guys? Please share your thought.
Now, go to the second page, and look for the highlighted equation. You will find this equation $[m/2] - [m/3] + 2 \geq p $. It doesn't make any sense to put square brackets around $m/2$ and $m/3$. So, according to me, this equation should look like eighter this $\lfloor m/2 \rfloor - \lfloor m/3 \rfloor + 2 \geq p$, or this $ \lceil m/2 \rceil - \lceil m/3 \rceil + 2 \geq p $, Which one of them, according to you guys? Please share your thoughts.
The second question is easily answered. The Kasami report was typed on an IBM Selectric typewriter which had a golfball head for ordinary letters and correspondence. The golfball head was exchangeable with a different golfball head for scientific notation (Greek alphabet, some symbols including $[$ and $]$ but not $\lfloor$ or $\rfloor$ or $\lceil$ or $\rceil$) and so Kasami had to make do with $[\cdot]$ instead of the more modern $\lfloor \cdot \rfloor$ that younger folks freely use. (Typing mathematics was particularly time-consuming because the heads had to be swapped in and out constantly). I know; I joined the Coordinated Science Laboratory of the University of Illinois in 1973 (about 5 years after Kasami returned to Japan) and IBM Selectrics were still in use for a decade or so until laser-printers become ubiquitous and small enough to fit on a desktop.
A more readable version of Kasami's results (and extensions thereof) can be found in Chapter 16 of Berlekamp's 1968 textbook Algebraic Coding Theory (McGraw-Hill but reprinted by other publishers since then).