I'm trying to come up with a conlang for a setting where spoken word casts magic etc. In this case, a group of wizards, etc. Develop arcadian, which functions to give the most information with the least amount of time spoken. I'm very new to conlangs, but I got a crude idea of how this could work. You start with a base, maybe a verb. Then, you add modifiers to designate direct objects, adjectives, etc. I know that this is pretty difficult, especially for a beginner. But, I'm hoping I can get some good tips and feedback on approaching this.
One already-existing conlang that goes in that direction is Ithkuil, a language made to compress information as much as possible, mainly by having a big number of phonemes (including tone) and short morphemes.
The most impressive example given by the author (in my opinion) is
Aukkras êqutta ogvëuļa tnou’elkwa pal-lši augwaikštülnàmbu.
‘An imaginary representation of a nude woman in the midst of descending a staircase in a step-by-step series of tightly-integrated ambulatory bodily movements which combine into a three-dimensional wake behind her, forming a timeless, emergent whole to be considered intellectually, emotionally and aesthetically.’
On the other hand, Ithkuil also strives for perfect exactness, so I'd suggest you could take some inspiration from it, but should cut e.g. some of the 96 cases, to make your language actually usable in practice.
First of all, natural languages seem to have a rather constant rate of information (measured in information per time), independent of genetic relations and of the typological classification of the language, for a scholarly reference see this answer on linguistics.se.
But as a conlang designer, you can strive for a higher information rate, specially when your conlang is used by people with some superhuman powers. As an example to achieve higher information rate, you may look at Dutton Speedwords.
This sounds like a bad idea to me. Redundancy (ie "superfluous" information) improves the robustness of transmission of a message, so while you can reduce it in artificial languages to increase the bandwidth, you trade this off against a higher rate of errors and failed transmissions.
Now imagine you had a list of spells, and in order to reduce the time needed to cast them, they are all abbreviated with a six-digit/letter code. Now you have a noisy environment, say during a storm or a battle, and you want to cast a particular spell. How likely is it that one of the letters or digits is coming across wrongly to the receiver of that spell? And then, instead of a fireball, you might create a bunch of flowers instead. Or you summon the wrong demon. There's a reason why phonetic alphabets ("alpha", "bravo", "charlie"...) exist. Similarly, a single spelling mistake (no pun intended) can achieve the same disastrous outcome in writing.
If you want to increase the robustness of your words, you could reduce the number of phonemes (as there is, say, no danger of confusing /k/ and /g/ if they don't make a distinction in your language); then either the words need to be longer (see eg some Hawai'ian words), or you need longer phrases (as you will have fewer words available that are not long) or multiple sentences (see eg toki pona).
Unfortunately there are certain quantitative properties of language (or any code for that matter) which cannot be overcome: you can't increase the amount of information transmitted without also increasing the danger of corrupting the message. Natural languages seem to have found a good balance over time to ensure adequate speed of information transmission overall.
If your message can be transmitted repeatedly (eg in a casual conversation), getting it wrong occasionally might not be a problem (as long as you notice it), but for a high-stakes, one-off communicative event (spell casting, military comms [see Charge of the Light Brigade], safety warnings, ...) I would want enough redundancy to make sure the message comes across correctly the first time.