46,375 reputation
359132
bio website users.utu.fi/lahtonen/…
location Rusko, Finland
age 50
visits member for 2 years, 10 months
seen 2 hours ago

General non-sense:

Mostly I teach here. I want to encourage beginning students to think for themselves, so I use a lot of hints and comments. More advanced questions I often just answer.

However, I don't do 1-on-1 chat. Don't ask. My answers and comments are for all to see, so I don't like to hide them. Also I feel that entering a chatroom carries with it an obligation to continue an on-line discussion, and then I would not be using my time on my own terms.

Relevant personal history:

PhD from Notre Dame in '90.

Drifted from representation theory of algebraic groups to applications of algebra into telecommunications, mostly coding theory, and lately mostly teaching at college level.

3 graduate students with awarded PhDs

I have mostly worked at our local University at Turku, Finland. At one point I tried working for Nokia Research Center. It was ok, but an old dog didn't learn all the tricks, and then they downsized, so I returned to the Uni as a tenured lecturer.


2h
revised Question about group theory and order in $\mathbb Z_n$
edited tags
2h
comment Order of groups and group elements?
Please read tag description before using them. Here order-theory is totally inappropriate, and that should be plain to you if you bothered to read its description.
2h
revised Order of groups and group elements?
edited tags
2h
reviewed Reject suggested edit on Question about group theory and order in $\mathbb Z_n$
4h
comment Subfield of the Galois Group of $x^5 - 1$
Quester: You do realize that Don Antonio's $\omega$= complex conjugation is your $\sigma^2$?
7h
comment The form of subrings of $k[[t]]$
Do you know what it means, when we assume that something is true?
13h
comment The form of subrings of $k[[t]]$
Why would you want to prove it? It is not true for all the rings! The book doesn't claim that it is!
14h
comment The form of subrings of $k[[t]]$
+1 for this. I really don't see this exercise in the book. The way I read it is that the closure property described here is assumed. The claim about the properties of the semigroup of values is the interesting consequence.
14h
comment The form of subrings of $k[[t]]$
Now that you copied the page from the book I understand this queation less! The author does not give this as an exercise nor does he claim it to be true. He just assumes that this holds. I would interpret this passage from the book as tellling that in what follows the author will only be interested in those subrings $H$ that have this closure property. At least that's how I read it.
1d
answered Multiplying in GF(128)
1d
revised Multiplying in GF(128)
edited tags
1d
comment The form of subrings of $k[[t]]$
You probably need $H$ to be a $k$-subalgebra, i.e. closed under scalar multiplication by elements of $k$? If so, then you can start with an arbitrary element $h\in H$, and keep subtracting the correct multiples of $S_{i_0}$, $S_{i_1}$ et cetera, so that the remainder always has a higher order.
2d
answered Subfields of irreducible polynomial fields with known dimensions
2d
comment Irreducibility of a Polynomial over Q
Newton's polygon should work here. Over 3-adics all the zeros of $p(x)$ have 3-adic (exponential) value $2/p$. For a product of a subset of any $s$ of them to be an integer, we need $2s/p$ to be an integer, i.e. we need $s=p$.
2d
revised reed muller code with parameters
edited tags
Apr
16
comment Can we find any relation between weight enumerator of code and dual code using graphs of both?
What do you mean with the phrase "relate the two using graph"?
Apr
16
revised Can we find any relation between weight enumerator of code and dual code using graphs of both?
edited body
Apr
16
comment If $\alpha$ and $\beta$ are algebraic integers then the roots of $x^2+\alpha x+\beta$ are algebraic integers
For all $i,j$ we have $x\alpha^i\beta^j\in x\Bbb{Z}[\alpha,\beta]$, and $x(x\alpha^i\beta^j)=x\alpha^{i+1}\beta^j+\alpha^i\beta^{j+1}\in \Bbb{Z}[\alpha,\beta]+x\Bbb{Z}[\alpha,\beta]$. By the assumption on $\alpha,\beta$ being algebraic we know that $\Bbb{Z}[\alpha,\beta]$ is a spanned by finitely many products of the form $\alpha^i\beta^j$, so that does it.
Apr
16
comment If $\alpha$ and $\beta$ are algebraic integers then the roots of $x^2+\alpha x+\beta$ are algebraic integers
Have you tried $W=\Bbb{Z}[x,\alpha,\beta]=\Bbb{Z}[\alpha,\beta]+x\Bbb{Z}[\alpha,\beta]$?
Apr
16
comment reed muller code with parameters
@Ross: It is common practice in coding theory for $(n,A,d)$ to denote a code of length $n$, $A$ words, and minimum distance $d$. There are other triplets in use with square brackets and a different meaning. $A$ is then replaced with $\log_2A$, so $(32,64,16)=[32,6,16]$. Anyway this matches the parameters of the $RM(1,5)$ Reed-Muller code. This code achieved lasting fame for its use by the Mariner probes. Those parameters of the Reed-Muller code $RM(r,m)$ are given in the right margin of that Wiki-article.