It has been known since [Zyablov and Pinsker, 1982] that a random q-ary code of rate 1-H q
(ρ)-ε (where 0<; ρ<; 1-1/q, ε>; 0 is small enough and-H q (·) is the g-ary entropy function) with …

We study certain combinatorial aspects of listdecoding, motivated by the exponential gap
between the known upper bound (of O (1/γ)) and lower bound (of Ω p (log (1/γ))) for the list …

There has been a great deal of work establishing that random linear codes are as list-
decodable as uniformly random codes, in the sense that a random linear binary code of rate …

There has been a great deal of work establishing that random linear codes are as list-
decodable as uniformly random codes, in the sense that a random linear binary code of rate …

We define the error exponent of the typical random code (TRC) as the long-block limit of the
negative normalized expectation of the logarithm of the error probability of the random code …

A family of error-correcting codes is list-decodable from error fraction $ p $ if, for every code
in the family, the number of codewords in any Hamming ball of fractional radius $ p $ is less …

A family of error-correcting codes is list-decodable from error fraction if, for every code in the
family, the number of codewords in any Hamming ball of fractional radius is less than some …

We study certain combinatorial aspects of list-decoding, motivated by the exponential gap
between the known upper bound (of O (1/γ)) and lower bound (of Ω p (log (1/γ))) for the list …

Some new results are derived concerning random coding error exponents and expurgated
exponents for list decoding with a deterministic list-size L. Two asymptotic regimes are …

We prove the following results concerning the list decoding of error-correcting codes: 1 We
show that for any code with a relative distance of δ (over a large enough alphabet), the …