Abstract We show that for a fixed $q$ , the number of -ary $t$ -error correcting codes length $n$ is at most $2^{(1 + o(1)) H_q(n,t)}$ all $t \leq (1 - q^{-1})n 2\sqrt{n \log n}$ where $H_q(n, t) = q^n/ V_q(n,t)$ Hamming bound and $V_q(n,t)$ cardinality radius ball. This proves conjecture Balogh, Treglown, Wagner, who showed result o(n^{1/3} (\log n)^{-2/3})$ .

A bstract We study M-theory compactified on twisted 7-tori with G 2 -holonomy. The effective 4d supergravity has 7 chiral multiplets, each a unit logarithmic Kähler potential. propose octonion, Fano plane based superpotentials, codifying the error correcting Hamming (4, 7) code. corresponding 7-moduli models have Minkowski vacua one flat direction. also superpotentials octonions/error codes for...

We consider dictionaries of size n over the finite universe u = (0, l)w and introduce a new technique for their implementation: error correcting codes. protected with an error-correcting code (ECC) is presented in this compared with the most recent implementation. treated within industries for their products. ―VLSI Implementation of Decoder Error Correcting in Satellite. Concatenation Code in F...