  We consider error-correction coding schemes for adversarial wiretap channels
(AWTCs) in which the channel can a) read a fraction of the codeword bits up to
a bound $r$ and b) flip a fraction of the bits up to a bound $p$. The channel
can freely choose the locations of the bit reads and bit flips via a process
with unbounded computational power. Codes for the AWTC are of broad interest in
the area of information security, as they can provide data resiliency in
settings where an attacker has limited access to a storage or transmission
medium.
  We investigate a family of non-linear codes known as pseudolinear codes,
which were first proposed by Guruswami and Indyk (FOCS 2001) for constructing
list-decodable codes independent of the AWTC setting. Unlike general non-linear
codes, pseudolinear codes admit efficient encoders and have succinct
representations. We focus on unique decoding and show that random pseudolinear
codes can achieve rates up to the binary symmetric channel (BSC) capacity
$1-H_2(p)$ for any $p,r$ in the less noisy region: $p<1/2$ and $r<1-H_2(p)$
where $H_2(\cdot)$ is the binary entropy function. Thus, pseudolinear codes are
the first known optimal-rate binary code family for the less noisy AWTC that
admit efficient encoders. The above result can be viewed as a derandomization
result of random general codes in the AWTC setting, which in turn opens new
avenues for applying derandomization techniques to randomized constructions of
AWTC codes. Our proof applies a novel concentration inequality for sums of
random variables with limited independence which may be of interest as an
analysis tool more generally.
