The way of turning 赤 into an adjective is adding い, but what does it mean when instead of a い you put a く？
I found it in this phrase:
I get the meaning but not the meaning of く.
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Keep in mind that Japanese "adjectives" function differently from English adjectives. You are in this case asking us about a い-adjective, 赤い. Those adjectives differ from the な-adjectives, for example 有名｛ゆうめい｝な:
い-adjectives are "conjugated", you can use them without modifying the copula (sometimes even remove it entirely)! In your example
is not a correct sentence.
Then, as mentioned in the related answer ～くありません is the polite form of ～くない. Thus, it is the polite negative form of the adjective.