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I have been recently studying Lie theory. I discovered that there is a family of Lie theoretic error correcting codes. I did not find any information except this paper:

So, my question is: why isn't there a further development of this research? Are these codes considered inefficient or impractical?

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There are zillions of papers in coding theory, proposing zillions of codes. Most of them are not used, due to several reasons:

  1. Some of the codes are non-constructive.

  2. Some of the codes don't have efficient decoding procedures.

  3. Some of the codes have bad parameters.

The main reason, however, is that practitioners don't spend their time reading the coding theory literature and thinking up applications of the various codes. Rather, given a concrete problem, they first look up the "standard" solutions they know of. I'm putting "standard" in quotes since different people probably use different types of codes — whatever they are used to. There are many reasons for this:

  1. Known codes are the easier to find out about — they are already familiar.

  2. Code (and sometimes hardware) is already available.

  3. Bosses prefer using known and proven tools.

  4. Practitioners are often interested in properties which are either hard to prove or are simply not completely formal, but could be tested experimentally (for example, recovery from burst errors). These are found in their own literature rather than the theoretical coding theory literature.

If none of the standard codes seem to work, then they are in trouble and probably ask an expert. The expert probably knows some other standard codes which do work.

For a new code or type of code to reach the mainstream requires a lot of publicity to make the community aware of it. Mathematicians working in coding theory don't usually care about the practical side, and indeed, often their constructions have theoretical aims which are not important in practice (this is especially common for researchers in theoretical computer science). Even if a particular code is practical, the researcher is usually not interested enough in promoting it for it to become widely known among the practitioners.

Engineers, on the other hand, might publish new practical codes, and rarely one of them does change the mainstream paradigm. Most papers are, however, small variations on known techniques, and are important mostly for people's resumes, or for the particular project they were developed for.

In your particular case, the paper you are linking to is theoretical, and ignores one of the main questions in coding theory, namely how to efficiently decode. This shows that it's a theoretical paper. The motivation behind the paper is to construct orthogonal codes with good parameters. It mentions that orthogonal codes have applications in mathematics, but not necessarily in "real life". Furthermore, as you mention, the construction seems novel, which makes it more interesting mathematically. Practically speaking, the novelty is not as important as the "usability" of the code in terms of parameters and ease of encoding and decoding, an issue not mentioned at all.

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    $\begingroup$ @p.s Something is up with your account. It looks like it did not link your account on CS with the question, so you aren't getting the rep points for the question. Not sure how to fix it though. $\endgroup$ – mikeazo May 20 '14 at 14:14

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